Design method for hyperchaotic circuit

Abstract

The invention provides a design method for a hyper-chaotic circuit, and the method comprises the steps: constructing a magnetic control memristor model and a magnetic control memristor model which have the hyper-chaotic characteristics correspondingly according to the characteristics of a magnetic control memristor and a magnetic control memristor; constructing a memristor-memristor hybrid hyperchaotic circuit model according to the constructed magnetic control memristor model and the magnetic control memristor model; and performing nonlinear dynamic behavior analysis on the constructed memristor-memristor hybrid hyperchaotic circuit model to determine the influence of the structure and circuit element parameters of the memristor-memristor hybrid hyperchaotic circuit on the memristor-memristor hybrid hyperchaotic circuit. The invention provides a circuit solution with higher safety and complexity for the fields of information processing, communication and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of digital circuits, and in particular, to a design method for a hyperchaotic circuit. Background Art

[0002] With the rapid development of technology, the generation and application of hyperchaotic phenomena have become research hotspots in multiple fields. In the field of the design of hyperchaotic circuits, many achievements have been made in the invention and design of memristors applied to chaotic circuits. For example, a design method for a fractional-order chaotic circuit based on a hybrid memristor (application number: CN202210133064.3), according to the Grunwald-Letnikov definition of fractional-order calculus, derives a fractional-order hybrid memristive chaotic circuit model from an integer-order circuit model, and uses 0-1 testing, SALI detection, Lyapunov exponents, and complexity methods to verify that the fractional-order circuit has complex nonlinear dynamic behaviors; combined with FPGA technology, fractional-order hybrid memristive chaotic models of the same order and different orders are designed, and the hardware simulation results are consistent with the numerical calculation results, which have broad application potential in the fields of complex dynamics and digital circuits.

[0003] Currently, although some achievements have been made in the application of memristors to chaotic circuits, such as the design method for a fractional-order chaotic circuit based on a hybrid memristor, in practical applications, it mainly focuses on a few specific types of memristors, and there are limitations in the application of other memristors with special properties and functions. Summary of the Invention

[0004] The present invention provides a design method for a hyperchaotic circuit to solve the defect that the potential advantages of a meminductor-memristor hybrid chaotic circuit cannot be fully utilized in the prior art.

[0005] On the one hand, the present invention provides a design method for a hyperchaotic circuit, including: Constructing corresponding magnetically controlled meminductor models and magnetically controlled memristor models with hyperchaotic characteristics according to the characteristics of magnetically controlled meminductors and magnetically controlled memristors; Constructing a meminductor-memristor hybrid hyperchaotic circuit model according to the constructed magnetically controlled meminductor models and magnetically controlled memristor models; and Performing a nonlinear dynamic behavior analysis on the constructed meminductor-memristor hybrid hyperchaotic circuit model to determine the influence of the structure and circuit element parameters of the meminductor-memristor hybrid hyperchaotic circuit on the meminductor-memristor hybrid hyperchaotic circuit.

[0006] The magnetically controlled meminductor model is represented by the following formula:

[0007] In the formula, The current represented as a magneto-controlled memristor, is the magnetic flux of the magneto-controlled memristor, is the voltage across the series connection of the magneto-controlled memristor and the negative conductance is the integral of the magnetic flux of the magneto-controlled memristor, and and are the actual parameters of the magneto-controlled memristor; The magneto-controlled memristor model is represented by the following formula:

[0008] wherein, is the memductance value of the magneto-controlled memristor, is the voltage across the magneto-controlled memristor, is the magnetic flux of the magneto-controlled memristor, and are the actual parameters of the magneto-controlled memristor.

[0009] Optionally, the state equation satisfied by the meminductor-memristor hybrid hyperchaotic circuit:

[0010] wherein the state parameters are , , , , , , The current represented as an inductor, is the magnetic flux of the magneto-controlled memristor, is the magnetic flux of the magneto-controlled memristor.

[0011] Optionally, when performing nonlinear dynamic behavior analysis on the constructed meminductor-memristor hybrid hyperchaotic circuit model, it includes: Using a numerical analysis tool, setting the analysis environment, and solving the dynamic equation of the meminductor-memristor hybrid hyperchaotic circuit model; Adjusting the key parameters in the meminductor-memristor hybrid hyperchaotic circuit model, and selecting preset parameter values in a stepwise increasing or decreasing manner; Setting the time step, tracking the evolution trajectories of multiple state variables in the meminductor-memristor hybrid hyperchaotic circuit model over time to obtain the time series data of the multiple state variables; Taking any two variables among the multiple state variables as coordinate axes, plotting the corresponding three-dimensional phase diagram to display the state changes of the meminductor-memristor hybrid hyperchaotic circuit model, calculating the Lyapunov exponent spectrum of the meminductor-memristor hybrid hyperchaotic circuit model, and determining the chaotic characteristics and stability of the meminductor-memristor hybrid hyperchaotic circuit model.

[0012] Optionally, the key parameters include capacitance value, inductance value, magnetically controlled memristor control parameters, and magnetically controlled meminductor parameters; The multiple state variables in the meminductor-memristor hybrid hyperchaotic circuit model include the voltages of the magnetically controlled meminductor and the magnetically controlled memristor at different nodes, and the currents flowing through different components in the meminductor-memristor hybrid hyperchaotic circuit model.

[0013] Optionally, analyzing the influence of the circuit element parameters on the meminductor-memristor hybrid hyperchaotic circuit includes: Traversing and analyzing different combinations of circuit element parameters, determining the variation ranges of each parameter, performing numerical simulations for each parameter combination, and obtaining the Lyapunov exponent spectrum; Gradually increasing any one of the parameter values of the magnetically controlled memristor and while fixing the other parameter value, obtaining the variation of the state variables of the meminductor-memristor hybrid hyperchaotic circuit model, and recording the change in the dynamic behavior; fixing the adjusted or value, gradually increasing the other parameter value of the magnetically controlled memristor and and repeating the above steps; Gradually increasing any one of the parameter values of the magnetically controlled meminductor and while fixing the other parameter value, determining the variation of the state variables of the meminductor-memristor hybrid hyperchaotic circuit model, and recording the changes in the shape, size, and structure of the chaotic attractor; for different values, gradually increasing the parameter value of the magnetically controlled meminductor value, and performing numerical simulation and analysis.

[0014] Optionally, when analyzing the influence of the circuit element parameters on the meminductor-memristor hybrid hyperchaotic circuit, it further includes: Based on the analysis results of the magnetically controlled memristor parameter values and the magnetically controlled meminductor parameter values, analyzing the influence of the circuit element parameters on the triggering and maintenance of the system's chaotic behavior and the shape and structure of the chaotic attractor.

[0015] Optionally, analyzing the complex dynamic behavior of the coexisting attractor phenomenon includes: By changing the values of the initial state variables of the meminductor-memristor hybrid hyperchaotic circuit model, determining whether the coexisting attractor phenomenon will occur in the meminductor-memristor hybrid hyperchaotic circuit model; Using numerical calculation and phase diagram analysis to determine the stability and conversion relationship between the coexisting attractors.

[0016] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the design method for the hyperchaotic circuit as described in any one of the above is implemented.

[0017] On the other hand, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the design method for the hyperchaotic circuit as described in any one of the above is implemented.

[0018] A design method for a hyperchaotic circuit provided by the present invention constructs a meminductor-memristor hybrid hyperchaotic circuit system composed of specific components and establishes an accurate meminductor-memristor hybrid hyperchaotic circuit model, achieving the following beneficial effects: An innovative hyperchaotic circuit structure is proposed, enriching the design methods and types of chaotic circuits.

[0019] The correctness of the theoretical analysis is verified through experiments, improving the reliability and practicality of the chaotic circuit design.

[0020] The multi-coexistence phenomenon of the meminductor-memristor hybrid hyperchaotic circuit system under different initial conditions is determined, providing a circuit solution with higher security and complexity for fields such as information processing and communication. Description of the Drawings

[0021] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0022] Figure 1 It is a schematic flowchart of a design method for a hyperchaotic circuit provided by an embodiment of the present invention.

[0023] Figure 2 It is a schematic diagram of the characteristic curves of a magnetically controlled meminductor and a magnetically controlled memristor constructed by the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 3 It is a schematic diagram of a six-dimensional memcapacitor-memristor hybrid hyperchaotic circuit constructed by the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 4 It is a schematic diagram of the time-domain waveform and the chaotic attractor of the hyperchaotic circuit system of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 5It is a schematic diagram of the initial conditions of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 6 They are the bifurcation diagram, the largest Lyapunov exponent spectrum, and the phase diagram of the hyperchaotic circuit system of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 7 They are the partition diagram of the largest Lyapunov exponent, the bifurcation diagram, and the phase diagram of the system with two-parameter control of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 8 It is the bifurcation diagram of the hyperchaotic circuit system of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 9 They are the attractor phase diagrams under different initial conditions of the design method for a hyperchaotic circuit provided by an embodiment of the present invention; Figure 10 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0025] Embodiment 1 Figure 1 It is a schematic flowchart of a design method for a hyperchaotic circuit provided by an embodiment of the present invention.

[0026] The design method for a hyperchaotic circuit provided by an embodiment of the present invention may be executed by an electronic device or a computer system with corresponding computing and processing capabilities. The method mainly includes the following steps: Step S110: Construct corresponding magnetically controlled meminductor models and magnetically controlled memristor models with hyperchaotic characteristics according to the characteristics of magnetically controlled meminductors and magnetically controlled memristors.

[0027] Step S120: Construct a meminductor-memristor hybrid hyperchaotic circuit model according to the constructed magnetically controlled meminductor models and magnetically controlled memristor models. Step S130: Perform a non-linear dynamic behavior analysis on the constructed meminductor-memristor hybrid hyperchaotic circuit model to determine the influence of the structure of the meminductor-memristor hybrid hyperchaotic circuit and the circuit element parameters on the meminductor-memristor hybrid hyperchaotic circuit.

[0028] In the first preferred embodiment of the present invention, the magneto-controlled memristor model can be expressed by the following formula: (1) Wherein, represents the current of the magneto-controlled memristor, is the magnetic flux of the magneto-controlled memristor, is the voltage across the series connection of the magneto-controlled memristor and the negative conductance , is the integral of the magnetic flux of the magneto-controlled memristor, and are the actual parameters of the magneto-controlled memristor, and their value ranges are set to ensure that the circuit system has chaotic characteristics. The parameters are set as α = 3 and β = -0.5. The voltage-current characteristic curve of the magneto-controlled memristor in the circuit is as shown in Figure 2 (a).

[0029] In the first preferred embodiment of the present invention, the magneto-controlled memristor model can be expressed by the following formula: (2) Wherein, is the memductance value of the magneto-controlled memristor, is the voltage across the memristor, is the magnetic flux of the memristor, and are the actual parameters of the memristor, and their value ranges are set to ensure that the system has chaotic characteristics. The parameters are set as γ = 1 and ε = 5. The voltage-current characteristic curve of the magneto-controlled memristor in the circuit is as shown in Figure 2 (b).

[0030] As shown in Figure 3 , a memristive-memristor hybrid chaotic circuit composed of the magneto-controlled memristor , the magneto-controlled memristor , the negative conductance G, the resistor R, the inductor L, and the two linear capacitors C1 and C2 is constructed. Analyzing its nonlinear dynamic behavior may include: According to Kirchhoff's law, as well as formula (1) and formula (2), the state equation satisfied by the memristive-memristor hybrid chaotic circuit is obtained and can be expressed by the following formula: (3) Wherein, the six state parameters are , , , , , ; Among them, represents the current of the inductor, is the magnetic flux of the memristor, is the magnetic flux of the memristor, let .

[0031] Preferably, according to the meminductor-memristor hybrid chaotic circuit system model, the parameters a = 1 / L, b = 1 / C1, c = 1 / C2, d = R, e = 1 / G, f = α, g = β, h = γ, j = ε can be selected, then the meminductor-memristor hybrid hyperchaotic circuit system model can be expressed as: (4); wherein, a, b, c, d, e, f, g, h, j are parameters. In order to ensure the best chaotic effect of the meminductor-memristor hybrid hyperchaotic circuit, the parameters are respectively set as a = 5.5, b = 15, c = 3, d = 0.2, e = 0.6, f = 3, g = -0.5, h = 1, j = 5. The analysis parameter values of the meminductor-memristor hybrid hyperchaotic circuit are the same as this below.

[0032] Based on the above scheme, the meminductor-memristor hybrid hyperchaotic circuit may further include: at least one sensor for real-time monitoring of at least one key parameter in the circuit, and the key parameter includes but is not limited to the inductor current , the voltage across the magneto-controlled memristor and the voltage across the series connection of the magneto-controlled meminductor and the negative conductance G ; a control unit, connected to the sensor, for receiving the key parameters collected by the sensor and generating a control signal according to a preset adaptive control algorithm; at least one variable element, connected to the control unit, for adjusting at least one parameter of the circuit according to the control signal, and the variable element includes but is not limited to a variable resistor for adjusting the negative conductance G, a variable capacitor for adjusting the capacitance C 1 or C 2 ; wherein, the adaptive control algorithm is based on at least one of the following methods: feedback linearization, model reference adaptive control, sliding mode control, fuzzy adaptive control, neural network adaptive control.

[0033] wherein, the control unit includes a processor and a storage unit, the storage unit is used for storing the adaptive control algorithm and related parameters, and the processor is used for executing the adaptive control algorithm.

[0034] wherein, the variable resistor is a digital potentiometer, and its resistance value is controlled by a digital signal, and the variable capacitor adopts a switched capacitor array.

[0035] In order to implement the adaptive control mechanism, sensors are added at key positions of the circuit. The specific connection method is that a current sensor is connected in series in the branch where the inductor L is located to monitor the inductor current ; A voltage sensor is connected in parallel across the memristor to monitor the voltage across the memristor. ; A voltage sensor is also connected in parallel across the two ends after the meminductor is connected in series with the negative conductance G to monitor the voltage. .

[0036] These sensors transmit the collected current and voltage signals to a control unit. The control unit contains an adaptive control algorithm that processes and calculates based on the received signals to generate control signals.

[0037] The control signals are respectively connected to some variable components to achieve the adjustment of circuit parameters. That is, by connecting a digital potentiometer across the two ends of the negative conductance G, the signal output by the control unit can change the resistance value of the digital potentiometer, thereby adjusting the magnitude of the negative conductance G; for capacitors C1 and C2, similar variable capacitor components can be used, or the capacitance value can be adjusted by means of a switched-capacitor array, etc.

[0038] More specifically, the adaptive control algorithm adopts a hybrid adaptive control algorithm, including a fuzzy logic part and a neural network part. The fuzzy logic partitions the circuit state based on the inductor current and the voltage of the magneto-controlled memristor. Among them, the inductor current partitioning method is as follows: When the inductor current is in an extremely low range below a specific threshold ) , the corresponding control strategy is to increase the inductor excitation source intensity or adjust the relevant capacitor parameters to change the resonance frequency.

[0039] When it is in a moderately low range ( ), the corresponding control strategy is to slightly adjust the resistance value to optimize the current distribution and energy transfer efficiency.

[0040] The voltage partitioning method of the magneto-controlled memristor is as follows: When the voltage of the magneto-controlled memristor is in a low and stable range ( ), the corresponding control strategy is to maintain the current circuit state and lock or slightly adjust the parameters of the surrounding components.

[0041] When the voltage of the magneto-controlled memristor is on the rise and approaching the critical value ( ), the corresponding control strategy is to quickly adjust the series or parallel components to avoid voltage breakthrough at the critical value, which may cause circuit instability. The fuzzy logic provides a macroscopic control strategy framework for the neural network.

[0042] The neural network part has a dynamic adjustment mechanism that operates based on circuit stability indicators and performance indicators. Among them, the stability indicators include the voltage output fluctuation amplitude, current smoothness, and voltage-current phase difference. When the voltage-current phase difference exceeds the preset range and is greater than ( ) or less than ) When, according to the pre-set algorithm and combined with the states of other circuit parameters, accurately calculate the adjustment amplitude of the number of hidden layer neurons; the performance indicators include the power conversion efficiency and are decomposed and evaluated for each sub-circuit module. When the power loss of a specific sub-circuit module, such as the sub-module composed of a memristor and a specific capacitor, suddenly increases, quickly adjust the control strategy weight of the relevant components of the module and increase the number of hidden layer neurons.

[0043] Moreover, the input information of the neural network part includes the environmental parameters after multi-sensor fusion. For the temperature information, establish a temperature-component performance relationship model according to the temperature characteristic curves of different components in the circuit. When the temperature changes, predict the change trend of the component performance according to this model and adjust the control strategy in advance; for the electromagnetic interference intensity information, use the pattern recognition ability of the neural network to distinguish the effects of electromagnetic interference with different frequency bands and intensities on different parts of the circuit and adjust the control strategy accordingly.

[0044] It also includes a reinforcement learning mechanism. This mechanism gives different reward or punishment signals according to the difference between the actual operating condition of the circuit and the expected operating state. When the control strategy makes the output voltage of the circuit accurately and stably at the set value and the current changes according to the predetermined law, give a positive reward signal to promote the optimization and adjustment of the neural network; when abnormal situations such as excessive power loss and serious signal distortion occur in the circuit, give a punishment signal to prompt the neural network to reflect and adjust the control strategy, including adjusting the connection weights between neurons, changing the signal transmission intensity, etc. to improve the control accuracy and response speed.

[0045] When performing non-linear dynamic behavior analysis on the constructed meminductor-memristor hybrid hyperchaotic circuit model, it includes: Using a numerical analysis tool (such as MATLAB), set up the analysis environment, and use a high-precision numerical integration method (such as the Runge-Kutta method) to solve the dynamic equation of the meminductor-memristor hybrid hyperchaotic circuit model.

[0046] Adjust the key parameters in the meminductor-memristor hybrid hyperchaotic circuit model in a step-by-step increasing or decreasing manner, and select the preset parameter values.

[0047] Set the time step, and track the evolution trajectories of multiple state variables in the meminductor-memristor hybrid hyperchaotic circuit model over time to obtain the time series data of multiple state variables.

[0048] For any two variables among the multiple state variables (for example, V 1 and I 1Taking [axis name] as the coordinate axes, plot the corresponding three-dimensional phase diagram to show the state changes of the meminductor-memristor hybrid hyperchaotic circuit model, calculate the Lyapunov exponent spectrum of the meminductor-memristor hybrid hyperchaotic circuit model, and determine the chaotic characteristics and stability of the meminductor-memristor hybrid hyperchaotic circuit model.

[0049] The specific process is as follows: Precisely change each key parameter in the circuit, including but not limited to capacitance values (such as C 1 , C 2 ), inductance values (such as L 1 , L 2 ), control parameters of the magneto-controlled memristor (such as and ), and relevant parameters of the magneto-controlled meminductor (such as and ). During the parameter adjustment process, use a step-by-step increasing or decreasing method and select representative parameter values for analysis to ensure comprehensive coverage of the parameter space.

[0050] At the same time, observe the evolution trajectories of multiple state variables in the meminductor-memristor hybrid hyperchaotic circuit system (for example, different node voltages V 1 , V 2 , etc., and currents I 1 , I 2 , etc.) flowing through different components over time. By setting an appropriate time step (such as 0.001 seconds) and using numerical integration methods such as Runge-Kutta, solve the dynamic equations of the meminductor-memristor hybrid hyperchaotic circuit system to obtain the time series data of the state variables.

[0051] Taking any two of the multiple state variables (for example, V 1 and I 1 ) as the coordinate axes, plot the corresponding three-dimensional phase diagram to show the state changes of the meminductor-memristor hybrid hyperchaotic circuit model, calculate the Lyapunov exponent spectrum of the meminductor-memristor hybrid hyperchaotic circuit model, and determine the chaotic characteristics and stability of the meminductor-memristor hybrid hyperchaotic circuit model.

[0052] It can be known that: The change in capacitance value has a significant impact on the chaotic behavior of the meminductor-memristor hybrid hyperchaotic circuit system. When the capacitance value (such as C 1When it is in a lower range (such as less than 1 nF), the meminductor-memristor hybrid hyperchaotic circuit system shows a faster convergence trend. The state variables gradually tend to stable values over time, and there are a small number of stable equilibrium points or limit cycles in the phase diagram, indicating that the meminductor-memristor hybrid hyperchaotic circuit system is in a relatively regular dynamic state. As the capacitance value gradually increases (for example, increases to 10 nF and above), the meminductor-memristor hybrid hyperchaotic circuit system begins to exhibit chaotic behavior. The phase diagram becomes complex and has no obvious pattern, and the state variables randomly jump within a certain range. At this time, the calculated maximum Lyapunov exponent is greater than zero, confirming that the meminductor-memristor hybrid hyperchaotic circuit system enters the chaotic state. Further increasing the capacitance value (such as reaching 100 nF), the chaotic behavior intensifies, the phase diagram becomes more diffuse and disordered, and multiple Lyapunov exponents are positive, indicating that the meminductor-memristor hybrid hyperchaotic circuit system reaches the hyperchaotic state.

[0053] The inductance value also plays a key role in the dynamic behavior of the meminductor-memristor hybrid hyperchaotic circuit system. When the inductance value (such as L 1 )varies within a certain specific interval (such as from 1 mH to 10 mH), the meminductor-memristor hybrid hyperchaotic circuit system can exhibit rich dynamic behaviors. At different values within this interval, the meminductor-memristor hybrid hyperchaotic circuit system may transition from a stable state to a chaotic state and then to a hyperchaotic state. Specifically, a smaller inductance value (such as 1 mH) may cause the meminductor-memristor hybrid hyperchaotic circuit system to be in a stable oscillation state, and the phase diagram shows regular periodic orbits; as the inductance value increases (such as 5 mH), chaotic phenomena gradually appear in the meminductor-memristor hybrid hyperchaotic circuit system, the complexity of the phase diagram increases, and the orbits become irregular; when the inductance value further increases (such as 10 mH), hyperchaotic behavior is obvious, multiple Lyapunov exponents are positive, and the phase diagram presents a highly complex structure, indicating that the dynamic behavior of the meminductor-memristor hybrid hyperchaotic circuit system becomes extremely complex and variable.

[0054] In this embodiment, analyzing the influence of the circuit element parameters on the meminductor-memristor hybrid hyperchaotic circuit includes: Traversing and analyzing different combinations of circuit element parameters, determining the variation range of each parameter, performing numerical simulation on each parameter combination, and obtaining the Lyapunov exponent spectrum.

[0055] Gradually increase the parameters of the magneto-controlled memristor and any one of the parameter values, fix the other parameter value, obtain the variation of the state variables of the meminductor-memristor hybrid hyperchaotic circuit model, and record the change in dynamic behavior; fix the adjusted or value, gradually increase the parameters of the magneto-controlled memristor and Another parameter value in it, and repeat the above steps.

[0056] Gradually increase the parameters of the magnetically controlled memristor and Any one of the parameter values in, fix the other parameter value, determine the change of the state variables of the memristive-memristive hybrid hyperchaotic circuit model, and record the changes in the shape, size, and structure of the chaotic attractor; for different values, gradually increase the parameters of the magnetically controlled memristor values, and conduct numerical simulation and analysis.

[0057] Specifically include: Through a high-precision numerical calculation method, traverse and calculate different combinations of circuit element parameters, and use the Lyapunov exponent spectrum of the memristive-memristive hybrid hyperchaotic circuit system as the main analysis index. First, determine the change range of each parameter. For example, the control parameter of the magnetically controlled memristor varies between 0.1 and 1, varies between 0.01 and 0.1, varies between 0.5 and 1.5, etc.; the parameters of the magnetically controlled memristor varies between 1 and 10, varies between 0.001 and 0.01, varies between 10 and 100, etc. For each parameter combination, conduct a long-term numerical simulation (such as the simulation time reaches 1000 seconds) to obtain an accurate Lyapunov exponent spectrum.

[0058] When studying the influence of the parameters of the magnetically controlled memristor on the memristive-memristive hybrid hyperchaotic circuit system, pay special attention to the parameters related to the rate of change of the resistance value with the magnetic field (such as and ). By gradually changing and values, observe the change of the state variables of the memristive-memristive hybrid hyperchaotic circuit system, and draw curves of state variables versus time, phase diagrams, Lyapunov exponent spectra, etc. For example, fix other parameters, first increase from 0.1 to 1 gradually, increasing by 0.1 each time, and record the change of the dynamic behavior of the memristive-memristive hybrid hyperchaotic circuit system at the same time; then fix the adjusted value, and change value in a similar way for another round of analysis.

[0059] For the magnetically controlled memristor, focus on studying the parameters related to the inductance change characteristics (such as and ) on the influence of the memristive-memristive hybrid hyperchaotic circuit system. When changing and When the value of, the long-term tracking and analysis of the state variables of the meminductor-memristor hybrid hyperchaotic circuit system are also carried out, and the changes in the shape, size, and structure of the chaotic attractor are observed. For example, is gradually increased from 1 to 10, with an increment of 1 each time, while keeping other parameters unchanged, and the changes in the dynamic behavior of the meminductor-memristor hybrid hyperchaotic circuit system are analyzed; then for different values, change from 10 to 100, with an increment of 10 each time, and detailed numerical simulations and analyses are carried out.

[0060] Based on the above content, the influence of the circuit element parameters on the meminductor-memristor hybrid hyperchaotic circuit can be obtained, including: The parameters related to the resistance change rate of the magneto-controlled memristor play a decisive role in triggering and maintaining the chaotic behavior of the meminductor-memristor hybrid hyperchaotic circuit system. When is relatively small (such as 0.1), the overall meminductor-memristor hybrid hyperchaotic circuit system is in a relatively stable state, the state variables change relatively smoothly with time, the phase diagram shows a simple trajectory, and the largest Lyapunov exponent in the Lyapunov exponent spectrum is close to zero or negative. As gradually increases (such as reaching 0.5), the meminductor-memristor hybrid hyperchaotic circuit system begins to exhibit chaotic behavior, the fluctuation amplitude of the state variables increases significantly, the phase diagram becomes complex and has an irregular shape, and at this time the largest Lyapunov exponent is greater than zero. When further increases (such as greater than 0.8), the chaotic behavior of the meminductor-memristor hybrid hyperchaotic circuit system intensifies, and hyperchaotic phenomena occur, with multiple positive Lyapunov exponents, indicating that the dynamic behavior of the meminductor-memristor hybrid hyperchaotic circuit system becomes extremely complex and the sensitivity to initial conditions is greatly enhanced.

[0061] The parameters of the memristor also have an important influence on the chaotic behavior of the meminductor-memristor hybrid hyperchaotic circuit system. When is relatively small (such as 0.01), similar to the case where is small, the meminductor-memristor hybrid hyperchaotic circuit system is relatively stable; as increases (such as reaching 0.05), chaotic behavior gradually appears, but it is different from the influence of the parameter . The change in the value mainly affects the shape and structure of the chaotic attractor. A smaller value makes the chaotic attractor relatively simple and compact, while a larger value (such as 0.1) will cause the chaotic attractor to become more complex and dispersed, and its fractal dimension also increases accordingly.

[0062] The parameters of the memristor greatly affect the shape and size of the chaotic attractor. When the value is small (such as 1), the shape of the chaotic attractor is relatively regular and the volume is small, and the range of activities of the state variables in the phase space is limited. As the value gradually increases (such as reaching 5), the shape of the chaotic attractor gradually becomes irregular, bifurcation and distortion phenomena appear, and the volume also increases accordingly, which means that the distribution of the state variables of the memristive - memristive hybrid hyperchaotic circuit system in the phase space is more extensive and complex. When the value further increases (such as 10), the structure of the chaotic attractor becomes highly complex, with rich details and fractal characteristics, indicating that the dynamic behavior of the memristive - memristive hybrid hyperchaotic circuit system becomes extremely complex and difficult to predict.

[0063] The parameters of the memristor mainly affect the rotation characteristics and period of the chaotic attractor. A smaller value (such as 10) makes the rotation speed of the chaotic attractor in the phase space slower and the period relatively longer; as the value increases (such as reaching 50), the rotation speed of the chaotic attractor speeds up and the period becomes shorter, and its trajectory in the phase space becomes denser and more complex. When the value further increases (such as 100), the periodic characteristics of the chaotic attractor become more obvious, but at the same time, it is accompanied by higher complexity and randomness, which reflects the multi - aspect regulation effect of the parameters on the dynamic behavior of the memristive - memristive hybrid hyperchaotic circuit system.

[0064] As described above, not only the specific influence of the parameters of each circuit element on the nonlinear dynamic behavior of the memristive - memristive hybrid hyperchaotic circuit system is obtained, but also a solid theoretical basis is provided for further optimizing the design and performance of the memristive - memristive hybrid hyperchaotic circuit system. By reasonably adjusting these parameters, precise control of the dynamic behavior of the memristive - memristive hybrid hyperchaotic circuit system can be achieved, enabling it to perform better in different application scenarios such as information encryption, modeling of complex memristive - memristive hybrid hyperchaotic circuit systems, and neural computing.

[0065] In this embodiment, the analysis of the complex dynamic behavior of the co - existing attractor phenomenon includes: By changing the values of the initial state variables of the memristive - memristive hybrid hyperchaotic circuit model, determining whether the co - existing attractor phenomenon will occur in the memristive - memristive hybrid hyperchaotic circuit model; Using numerical calculation and phase diagram analysis to determine the stability and conversion relationship between the co - existing attractors.

[0066] Adopting the numerical simulation method, changing the values of the initial state variables of the memristive - memristive hybrid hyperchaotic circuit system. For each state variable in the circuit (such as the node voltage V 1 、V 2 、V3 etc., and the current I 1 、I 1 etc.), are offset within their respective possible value ranges. The variation range of the initial value is set according to the actual situation. For example, for voltage variables, it varies within the range from -50% to +50% of the normal operating value, and the step size of each change is 5% of the normal operating value of the variable.

[0067] For each combination of initial conditions, a long-term numerical simulation is carried out (for example, the simulation time reaches 2000 seconds) to ensure that the memristive-memristive hybrid hyperchaotic circuit system can fully evolve and exhibit stable dynamic behavior. Closely track the time evolution trajectory of the state variables of the memristive-memristive hybrid hyperchaotic circuit system, and observe whether the coexisting attractor phenomenon appears in the memristive-memristive hybrid hyperchaotic circuit system. At the same time, record the type of attractor (stable equilibrium point, limit cycle or chaotic attractor) that the memristive-memristive hybrid hyperchaotic circuit system converges to when it reaches a stable state (the state variables no longer change within a given error range).

[0068] Using bifurcation theory and numerical analysis techniques, accurately quantify the stability and conversion relationship between coexisting attractors. Draw a bifurcation diagram, with a parameter (such as a key circuit element parameter or etc. ) as the horizontal axis, and a characteristic quantity of the state variables of the memristive-memristive hybrid hyperchaotic circuit system (such as the voltage amplitude at a specific node) as the vertical axis. By changing the parameter value and observing the change of the state variables of the memristive-memristive hybrid hyperchaotic circuit system, determine the position and type of the bifurcation point (such as period-doubling bifurcation, Hopf bifurcation, etc.). At the same time, draw an attractor basin of attraction diagram, with two state variables (such as V 1 and V 2 ) as the coordinate axes, and different color regions represent the types of attractors that the memristive-memristive hybrid hyperchaotic circuit system finally converges to under different initial conditions, thus intuitively showing the boundaries and stability regions between coexisting attractors.

[0069] Further analyze the conversion mechanism between coexisting attractors. By introducing external interference signals (such as small-amplitude noise signals or periodic pulse signals), observe the process and conditions of the memristive-memristive hybrid hyperchaotic circuit system switching from one attractor to another under the action of interference. Analyze the influence of parameters such as the frequency, amplitude, and action time of the interference signal on the attractor conversion, and quantitatively describe characteristics such as the probability and time scale of the attractor conversion.

[0070] As described above, in the embodiments of the present invention, when the circuit element parameters are within a specific value range, the meminductor-memristor hybrid hyperchaotic circuit system will exhibit a remarkable phenomenon of coexistence of multiple chaotic attractors or stable equilibrium points. For example, when the memristor parameter takes values such as from 0.5 to 0.8, takes values such as from 0.05 to 0.1, and the meminductor parameter takes values such as from 3 to 7 and from 20 to 50, and at the same time, the initial state variables of the circuit are changed (for example, the initial voltage varies between -1V and +1V), it will be found that the meminductor-memristor hybrid hyperchaotic circuit system can converge to multiple different chaotic attractors or stable equilibrium points under different initial conditions. These coexisting attractors have different shapes and positions in the phase space, with complex and diverse shapes, and may exhibit different structures such as single-scroll, double-scroll or multi-scroll, and have a certain stability within their respective basins of attraction.

[0071] By plotting the bifurcation diagram and the attractor basin of attraction diagram, the stability and conversion relationship between the coexisting attractors can be clearly revealed. The bifurcation diagram shows that as the key parameters (such as or ) gradually change, the meminductor-memristor hybrid hyperchaotic circuit system will undergo a series of bifurcation processes, and at the bifurcation points, the stability of the meminductor-memristor hybrid hyperchaotic circuit system changes, and it may switch from one stable attractor to another. For example, when gradually increases from 20 to 50, the meminductor-memristor hybrid hyperchaotic circuit system will undergo multiple period-doubling bifurcations and Hopf bifurcations, resulting in significant changes in the structure and stability of the chaotic attractors. The attractor basin of attraction diagram intuitively shows the types of attractors that the meminductor-memristor hybrid hyperchaotic circuit system finally converges to under different initial conditions, as well as the boundary conditions between the coexisting attractors. It can be found that in some boundary regions, the meminductor-memristor hybrid hyperchaotic circuit system is extremely sensitive to the initial conditions, and a slight change in the initial value may cause the meminductor-memristor hybrid hyperchaotic circuit system to converge to different attractors, which reflects the complexity and uncertainty of the coexisting attractor phenomenon.

[0072] It can be seen that external interference signals have an important impact on the conversion between coexisting attractors. When a small-amplitude noise interference signal is introduced (for example, Gaussian white noise with an amplitude of 0.01 V), the meminductor-memristor hybrid hyperchaotic circuit system will switch from one chaotic attractor to another chaotic attractor with a certain probability. As the noise amplitude increases (such as increasing to 0.1 V), this conversion probability also increases accordingly, but at the same time, the overall stability of the meminductor-memristor hybrid hyperchaotic circuit system will be affected to a certain extent. For periodic pulse interference signals, their frequency and amplitude also play a key role in the attractor conversion. When the pulse frequency is close to the natural frequency of the meminductor-memristor hybrid hyperchaotic circuit system and the amplitude is moderate (such as the frequency is 1.2 times the natural frequency of the meminductor-memristor hybrid hyperchaotic circuit system and the amplitude is 0.05 V), it can effectively trigger the conversion between attractors. Too high or too low frequency, too large or too small amplitude will lead to a decrease in the conversion probability or an extension of the conversion time. This provides a theoretical basis for further determining how to use external interference to control and regulate the dynamic behavior of the meminductor-memristor hybrid hyperchaotic circuit system.

[0073] In summary, the coexisting attractor phenomenon and its complex dynamic behavior exhibited by the meminductor-memristor hybrid hyperchaotic circuit model under specific conditions not only enrich our understanding of the hyperchaotic meminductor-memristor hybrid hyperchaotic circuit system, but also provide broad application space and potential application value for its applications in frontier fields such as multi-modal information processing, complex meminductor-memristor hybrid hyperchaotic circuit system modeling, high-performance encryption communication, and neural network computing. By deeply analyzing these complex dynamic behaviors and their regulation mechanisms, it is possible to provide theoretical guidance and technical support for the development of more efficient, safer, and more intelligent meminductor-memristor hybrid hyperchaotic circuit systems.

[0074] Embodiment 2 The present invention also provides an implementation step of a design method for a hyperchaotic circuit according to Embodiment 1: Based on the method steps of Embodiment 1, the following will be described in combination with Figures 1 - 9 for description.

[0075] Perform a dynamic characteristic analysis on the invention system (the meminductor-memristor hybrid hyperchaotic circuit system, hereinafter referred to as the system), calculate the divergence ▽V < 0 of the system. This system is a dissipative system, and its non-linear dynamic behavior converges according to a certain exponential level when t approaches infinity; every point on the φRm−ρLm plane is an equilibrium point. Using the Routh-Hurwitz criterion theorem, the equilibrium points of the system are all unstable equilibrium points, that is, chaotic phenomena will occur. The Lyapunov exponents of the system calculated by the Jacobi method are, for example, λ1 = 0.7830, λ2 = 0.2688, λ3 = -0.1291, λ4 = -0.3406, λ5 = -4.3724, λ6 = -25.7779. Therefore, it can be determined that the system of the present invention is in a hyperchaotic state; the calculated Lyapunov dimension is 4.1331, which is a fractional dimension, further indicating that the system is chaotic.

[0076] For example, the initial condition I 0 = (x 0 , y 0 , z 0 , w 0 , u 0 , l 0 ) = (1, 1, 1, 1, 1, 1), and using the fourth-fifth order Runge-Kutta algorithm, the time-domain diagram of the system is simulated (as shown in Figure 4 a - b) and the chaotic attractor as shown in Figure 4 c - d, where: (a) w - t; (b) u - t; (c) z - y attractor; (d) l - u - x attractor), which confirms that the system is a chaotic system with ergodicity and boundedness.

[0077] Calculate the power spectrum of the inventive system, as shown in Figure 5 a continuous but non-smooth curve, indicating that the system is in a chaotic state and the dynamic behavior is relatively complex; for example, taking the cross-section of x and z on y = 0 and drawing the Poincaré section, as shown in Figure 5 b, which are some dense points in a certain area, further confirming that the system is in a chaotic state. Figure 5 Among them, I0 = (1, 1, 1, 1, 1, 1), and the power spectra of different variables (x, y, z, w, u, l) when the parameters are (a, b, c, d, e, f, g, h, j) = (5.5, 15, 3, 0.2, 0.6, 3, -0.5, 1, 5), where: a) The power spectrum of the system; (b) The Poincaré section of y = 0.

[0078] The following effects of the circuit element parameters on the system are obtained: 1. Changing the parameter of the inductor L (where a = 1 / L), with other parameters remaining unchanged, and the initial condition of the circuit being (x0, y0, z0, w0, u0, l0) = (1, 1, 1, 1, 1, 1). Among them, a ∈ [5.5, 9.0]. Figure 6 a) shows the bifurcation diagram varying with the parameter a. Figure 6(b) Maximum Lyapunov exponent spectrum. The two correspond very well, showing the complete inverse bifurcation process: the evolution process from the chaotic state through period-doubling bifurcation to the periodic state and finally returning to the equilibrium point state, and a periodic window appears near a = 6.1.

[0079] 2. Continuing as Figure 6 shown, where (a - b) are for b = 15; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5, and the bifurcation diagram and maximum Lyapunov exponent spectrum of the system when a ∈ [5.5, 9]; (c - d) are for a = 5.5; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5, and the bifurcation diagram and maximum Lyapunov exponent spectrum of the system when b ∈ [1, 15]; (e) is the phase diagram of the system when a = 6.4; b = 15; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5; (f) is the phase diagram of the system when a = 6.8; b = 15; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5; (g) is the phase diagram of the system when a = 7.5; b = 15; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5; (h) is the phase diagram of the system when a = 8.8; b = 15; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5. By changing the parameter of capacitor C1 (where b = 1 / C1) and keeping other parameters unchanged, the initial conditions of the circuit are (x0, y0, z0, w0, u0, l0) = (1, 1, 1, 1, 1, 1). Where b ∈ [2.1, 5.9]. Figure 6 (c) shows the bifurcation diagram varying with parameter b, Figure 6 (d) Maximum Lyapunov exponent spectrum. The two correspond very well, showing the complete period-doubling bifurcation process: the evolution process from the equilibrium point to the periodic state and finally entering the chaotic state through period-doubling bifurcation.

[0080] 3. For example, let a take values 6.4, 6.8, 7.5, 8.8, and simulate the attractor diagrams of the system, such as Figure 6 (e - h), which Figure 6 corresponds consistently with the maximum Lyapunov exponent spectrum of parameter a in

[0081] Conduct a deeper analysis of the dynamic effects on this circuit system when multiple parameters change simultaneously.

[0082] 1. For example, when the parameters are set as \(c = 3\), \(d = 0.2\), \(e = 0.6\), \(f = 3\), \(g=-0.5\), \(h = 1\), \(j = 5\), and \(a\in[5.5,9.0]\) and \(b\in[0,15.5]\) vary simultaneously in their respective intervals, calculate the maximum Lyapunov exponent of the system, represent the high and low of the exponent with different colors, and draw a "two-dimensional parameter space" diagram, as Figure 7 (a); Observing horizontally along \(a = 5.5\), it can be observed that when \(b\) enters the periodic state from the equilibrium state near 2 and changes from periodic to chaotic near 6, which basically corresponds to the maximum Lyapunov exponent spectrum of the system when varying with the single parameter \(b\) as shown in Figure 6 (d); Similarly, when observing the variation state of parameter \(a\) vertically when \(b = 15\), when \(a\) varies in the interval \([5.5,6.77]\), the system is mostly in the chaotic state, with a short periodic interval appearing in the middle. When \(a\) is in \([6.77,8.29]\), the system is in the periodic state, and then enters the equilibrium state when going further up, which basically corresponds to the maximum Lyapunov exponent spectrum of the system when varying with the single parameter \(a\) as shown in Figure 6 (b).

[0083] 2. As Figure 7 shown, where: (a) Partition diagram of the maximum Lyapunov exponent of the system under two-parameter control; (b) Bifurcation diagram of the system when \(b = 10\); \(c = 3\); \(d = 0.2\); \(e = 0.6\); \(f = 3\); \(g=-0.5\); \(h = 1\); \(j = 5\), and \(a\in[5.5,9]\); (c) Phase diagram of the system when \(a = 6\), \(b = 10\); \(c = 3\); \(d = 0.2\); \(e = 0.6\); \(f = 3\); \(g=-0.5\); \(h = 1\); \(j = 5\); (d) Phase diagram of the system when \(a = 6.7\), \(b = 10\); \(c = 3\); \(d = 0.2\); \(e = 0.6\); \(f = 3\); \(g=-0.5\); \(h = 1\); \(j = 5\); (e) Phase diagram of the system when \(a = 7.5\), \(b = 10\); \(c = 3\); \(d = 0.2\); \(e = 0.6\); \(f = 3\); \(g=-0.5\); \(h = 1\); \(j = 5\); (f) Phase diagram of the system when \(a = 8.5\), \(b = 10\); \(c = 3\); \(d = 0.2\); \(e = 0.6\); \(f = 3\); \(g=-0.5\); \(h = 1\); \(j = 5\); With other parameters unchanged, calculate the maximum Lyapunov exponent spectrum of \(b = 10\), \(a\in[5.5,9.0]\), as shown in Figure 7 (b). The parameter \(a\) ends the chaotic state and enters the periodic state around 6.6, and then ends the periodic state and enters the equilibrium state around 7.8, which corresponds to what is shown in Figure 7 (a).

[0084] 3. Verification of the phase diagram of the simulation of four pairs of a and b parameters and the "two-dimensional parameter space" diagram. With other parameters unchanged, when a = 6 and b = 10, the system is in a chaotic state, as shown in Figure 7 (c); with other parameters unchanged, when a = 6.7 and b = 10, the system is in a quasi-periodic state, as shown in Figure 7 (d); with other parameters unchanged, when a = 7.5 and b = 10, the system is in a multi-periodic state, as shown in Figure 7 (c); with other parameters unchanged, when a = 7.5 and b = 10, as shown in Figure 7 (f) shows the process of the system gradually evolving to the equilibrium state. The images generated by the above parameter changes are consistent with the states shown in the dynamic map and bifurcation diagram.

[0085] Select the coexisting attractor phenomenon and other complex dynamic behaviors of the memristor-memristive hybrid hyperchaotic system model under different initial conditions to demonstrate the sensitivity of the system to the initial conditions.

[0086] 1. As Figure 8 shown, where: (a) Bifurcation diagram of the system when a = 5.5; b = 10; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5, and the initial condition is (1,1, 1, 1, 1, l(0)) with l(0) ∈ [1, 3.5]; (b) Bifurcation diagram of the system when a = 5.5; b = 10; c = 3; d = 0.2; e = 0.6; f = 3; g = -0.5; h = 1; j = 5, and the initial condition is (1, 1,1, 1, u(0), 1) with u(0) ∈ [0.3, 1]; Set the initial value I0 = (x0,y0,z0,w0,u0,l0) = (1,1,1,1,1,l(0)), and when l(0) varies in the interval [1, 3.8], the bifurcation diagram of the simulation system, as Figure 8 (a); set the initial value I0 = (x0,y0,z0,w0,u0,l0) = (1,1,1,1,u(0),1), and when u(0) varies in the interval [0.3, 1], the bifurcation diagram of the simulation system, as Figure 8 (a), it can be seen that the system exhibits complex dynamic behaviors under different initial conditions.

[0087] 2. Simulate the attractor phase diagram of the invention system under different initial conditions.

[0088] Table 1 Correspondence table between different initial conditions and attractors

[0089] The phase diagrams of systems with different initial conditions are shown respectively, and Table 1 lists the corresponding initial conditions and the types of coexisting attractors. Figure 9 (a)The coexistence of a limit cycle and an equilibrium point respectively, and the two attractors are presented by trajectories of two colors on one graph; Figure 9 (b)The coexistence of two non - coincident limit cycles; Figure 9 (c)The coexistence of a chaotic attractor and an equilibrium point at the center; Figure 9 (d)The coexistence of a chaotic attractor and a limit cycle in the middle; Figure 9 (e)The coexistence of two chaotic attractors.

[0090] Figure 10 It is a schematic structural diagram of an electronic device provided by an embodiment of the present invention.

[0091] As Figure 10 shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 640. Among them, the processor 610, the communication interface 620, and the memory 630 complete communication with each other through the communication bus 640. The processor 610 can call the logical instructions in the memory 630 to execute the design method for the hyper - chaotic circuit.

[0092] In addition, when the logical instructions in the above - mentioned memory 630 are implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a computer - readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. And the aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read - only memories (ROM, Read - Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0093] On the other hand, the present invention also provides a computer program product. The computer program product includes a computer program. The computer program can be stored on a non - transitory computer - readable storage medium. When the computer program is executed by a processor, the computer can execute the design method for the hyper - chaotic circuit provided by the above - mentioned methods.

[0094] In another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is used to implement the design method for a hyperchaotic circuit provided by the above-mentioned various methods.

[0095] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative labor.

[0096] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a hyperchaotic circuit, characterized in that: include: According to the characteristics of magnetically controlled memristors and magnetically controlled memristors, corresponding magnetically controlled memristor models and magnetically controlled memristor models with hyperchaotic characteristics are constructed; According to the constructed magnetically controlled memristor model and magnetically controlled memristor model, a memristor-memristor hybrid hyperchaotic circuit model is constructed; and The nonlinear dynamic behavior analysis of the constructed memsensor-memristor hybrid hyperchaotic circuit model is performed to determine the influence of the structure of the memsensor-memristor hybrid hyperchaotic circuit and the circuit element parameters on the memsensor-memristor hybrid hyperchaotic circuit.

2. The design method for a hyperchaotic circuit according to claim 1, characterized in that: The magnetically controlled memristor model is expressed by the following formula: In the formula, is the current of the magnetically controlled memristor, is the magnetic flux of the magnetically controlled memristor, Magnetic memristor and negative conductance The voltage across the two ends after series connection is is the integral of the magnetic flux of the magnetically controlled memristor, and are the actual parameters of the magnetically controlled memristor; The magnetically controlled memristor model is expressed by the following formula: In the formula, is the memristor value of the magnetically controlled memristor, is the voltage across the magnetically controlled memristor, is the magnetic flux of the magnetically controlled memristor, and are the actual parameters of the magnetically controlled memristor.

3. The design method for a hyperchaotic circuit according to claim 1, characterized in that: The state equation satisfied by the memsensory-memristor hybrid hyperchaotic circuit is: In the formula, the state parameter is , , , , , , is the current in the inductor, is the magnetic flux of the magnetically controlled memristor, is the magnetic flux of the magnetically controlled memristor.

4. The design method for a hyperchaotic circuit according to claim 2, characterized in that: The nonlinear dynamic behavior analysis of the constructed memsensory-memristor hybrid hyperchaotic circuit model includes: Use numerical analysis tools to set up the analysis environment and solve the dynamic equations of the memristor-memristor hybrid hyperchaotic circuit model; Adjust key parameters in the memristor-memristor hybrid hyperchaotic circuit model, and select preset parameter values ​​in a step-by-step increasing or decreasing manner; Setting a time step to track the evolution of multiple state variables in the memristor-memristor hybrid hyperchaotic circuit model over time to obtain time series data of the multiple state variables; Taking any two variables among the multiple state variables as coordinate axes, draw the corresponding three-dimensional phase diagram to show the state change of the memsensor-memristor hybrid hyperchaotic circuit model, and calculate the Lyapunov index spectrum of the memsensor-memristor hybrid hyperchaotic circuit model to determine the chaotic characteristics and stability of the memsensor-memristor hybrid hyperchaotic circuit model.

5. The design method for a hyperchaotic circuit according to claim 4, characterized in that: The key parameters include capacitance value, inductance value, magnetically controlled memristor control parameters and magnetically controlled memristor parameters; The multiple state variables in the memristor-memristor hybrid hyperchaotic circuit model include the voltages of the magnetically controlled memristor and the magnetically controlled memristor at different nodes, and the currents flowing through different elements in the memristor-memristor hybrid hyperchaotic circuit model.

6. The design method for a hyperchaotic circuit according to claim 1, characterized in that: Analyzing the influence of the circuit element parameters on the memsensory-memristor hybrid hyperchaotic circuit includes: Traverse and analyze different combinations of circuit component parameters, determine the range of variation of each parameter, perform numerical simulation on each parameter combination, and obtain the Lyapunov index spectrum; Gradually increase the parameters of the magnetically controlled memristor and Any parameter value in the equation is set, and another parameter value is fixed to determine the change of the state variable of the memristor-memristor hybrid hyperchaotic circuit model, and record the change of the dynamic behavior; fix the adjusted or value, gradually increase the magnetic controlled memristor parameters and Repeat the above steps for another parameter value; Gradually increase the parameters of the magnetically controlled memristor and Take any parameter value in the equation, fix the other parameter value, determine the change of state variables of the memristor-memristor hybrid hyperchaotic circuit model, and record the change of shape, size and structure of the chaotic attractor; value, gradually increase the magnetic control memristor parameters values, and conduct numerical simulation and analysis.

7. The design method for a hyperchaotic circuit according to claim 6, characterized in that: When analyzing the influence of the circuit element parameters on the memsensory-memristor hybrid hyperchaotic circuit, it also includes: According to the analysis results of the parameter values ​​of the magnetically controlled memristor and the magnetically controlled memsensor, the influence of the circuit component parameters on the triggering and maintenance of the chaotic behavior of the system as well as the shape and structure of the chaotic attractor is analyzed.

8. The design method for a hyperchaotic circuit according to claim 3, characterized in that: Analysis of complex dynamical behaviors of coexisting attractor phenomena includes: By changing the value of the initial state variable of the memsensory-memristor hybrid hyperchaotic circuit model, determining whether the memsensory-memristor hybrid hyperchaotic circuit model will have a coexistence attractor phenomenon; Numerical calculations and phase diagram analysis are used to determine the stability and transformation relationships between coexisting attractors.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the design method for a hyperchaotic circuit as claimed in any one of claims 1 to 8 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the design method for a hyperchaotic circuit as claimed in any one of claims 1 to 8 is implemented.

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