An isomorphic neuronal system generating a hidden coexisting attractor

Abstract

The application discloses a kind of isomorphic neuron system for generating hidden coexisting attractor, it is related to neuromorphic computing and nonlinear circuit field, the system includes: memristor, first neuron network and second neuron network;The structure of the first neuron network and the second neuron network is identical;Synaptic connection is carried out between the first neuron network and the second neuron network by the memristor, to simulate the chaotic dynamic behavior of biological neuron, to generate hidden coexisting attractor.The application can accurately simulate the synaptic transmission characteristics of biological neuron, improve the authenticity of bionics, successfully reproduce the chaotic dynamic behavior of biological neuron, efficiently generate hidden coexisting attractor, and enrich the dynamic performance of neuron system.

Description

Technical Field

[0001] This application relates to the fields of neuromorphic computing and nonlinear circuits, and in particular to an isomorphic neuron system that generates hidden coexistence attractors. Background Technology

[0002] Existing neural network circuits mostly employ single models (such as the Hindmarsh-Rose model or the Rulkov model) and linear synaptic coupling mechanisms, making it difficult to accurately reflect the synaptic plasticity of biological neural networks. Analysis of coupling mechanisms between structurally similar subnetworks is fragmented and lacks systematic research. On the other hand, research on high-dimensional neural networks largely focuses on utilizing their hyperchaotic properties for encryption applications, with relatively insufficient exploration of the dynamics arising from inter-network interactions. Although existing research has improved computational efficiency by optimizing circuit parameters and structures, challenges remain in multistable state control, hidden attractor generation, and accurate simulation of synaptic plasticity. Hardware implementation of high-dimensional neural networks often faces problems such as high complexity, high power consumption, and uncontrollable multistable states, limiting their application in neuromorphic computing and brain-computer interfaces. Summary of the Invention

[0003] The purpose of this application is to provide an isomorphic neuron system that generates hidden coexistence attractors, which can simulate the chaotic dynamics of biological neurons and generate hidden coexistence attractors.

[0004] To achieve the above objectives, this application provides an isomorphic neuronal system for generating hidden coexistence attractors, comprising: a memristor, a first neuronal network, and a second neuronal network; the first neuronal network and the second neuronal network have the same structure; the first neuronal network and the second neuronal network are synaptactically connected through the memristor to simulate the chaotic dynamics of biological neurons and generate hidden coexistence attractors.

[0005] In one embodiment, the memristor is an ideal flux-controlled memristor with cosine reactance.

[0006] In one embodiment, the expression for the ideal flux-controlled memristor with cosine reactance is: ;in, i For current, v For voltage, For the sake of memory, For magnetic flux, for The first derivative, It is a state variable.

[0007] In one embodiment, both the first neural network and the second neural network are three-dimensional Hopfield neural networks.

[0008] In one embodiment, the expressions for the first neural network and the second neural network are: ;in, x k For neurons k membrane potential, x j For neurons j membrane potential, C k For neurons k Capacitance inside and outside the cell, R k For neurons k Membrane resistance inside and outside the cell, n For the number of neurons, w kj For neurons k With neurons j Synaptic weights, determined by neurons k With neurons j The strength of the connection between them determines, I k For neurons k Input bias current 。

[0009] In one embodiment, both the first neural network and the second neural network include three neurons.

[0010] In one embodiment, the mathematical equation of the isomorphic neuron system is: ;in, This represents the membrane potential of the first neuron in the first neuron network. This represents the membrane potential of the second neuron in the first neuronal network. This represents the membrane potential of the third neuron in the first neuron network. This represents the membrane potential of the first neuron in the second neuronal network. This represents the membrane potential of the second neuron in the second neuron network. This represents the membrane potential of the third neuron in the second neuronal network. For magnetic flux, t Let g be time, g1 be the self-coupling strength of the first neuron in the first neuron network and the second neuron network, g2 be the coupling strength between the second neuron and the first neuron in the first neuron network and the second neuron network, and g3 be the coupling strength between the third neuron and the first neuron in the first neuron network and the second neuron network.

[0011] In one embodiment, the mathematical equations of the isomorphic neuron system are implemented based on capacitors, resistors, operational amplifiers, analog multipliers, and function generators; wherein, capacitors and resistors are used to control the values ​​of g1, g2, and g3, operational amplifiers are used to perform integral operations, analog multipliers are used to perform nonlinear operations, and function generators are used to perform trigonometric function operations.

[0012] In one embodiment, the circuit for implementing the mathematical equations of the isomorphic neuron system includes... Side roads Side roads Side roads Side roads Side roads branch roads and Branch circuits; each branch circuit includes capacitors, resistors, operational amplifiers, analog multipliers, and function generators.

[0013] In one implementation, The circuit equation for the branch is:

[0014] ;

[0015] The circuit equation for the branch is:

[0016] ;

[0017] The circuit equation for the branch is:

[0018] ;

[0019] The circuit equation for the branch is:

[0020] ;

[0021] The circuit equation for the branch is:

[0022] ;

[0023] The circuit equation for the branch is:

[0024] ;

[0025] The circuit equation for the branch is:

[0026] ;

[0027] in, C 1 is the first capacitor. C2 is the second capacitor. C 3 is the third capacitor. C 4 is the fourth capacitor. C 5 is the fifth capacitor. C 6 is the sixth capacitor. C 7 is the seventh capacitor. R 1 represents the first resistor. R 2 is the second resistor. R 3 is the third resistor. R 4 is the fourth resistor. R 5 is the fifth resistor. R 6 is the sixth resistor. R 7 is the seventh resistor. R 8 represents the eighth resistor. R 9 is the ninth resistor. R 10 The tenth resistor, R 11 The eleventh resistor, R 12 The twelfth resistor, R 13 The thirteenth resistor, R 14 This is the fourteenth resistor. R 15 This is the fifteenth resistor. R 16 This is the sixteenth resistor. R 17 This is the seventeenth resistor. R 18 This is the eighteenth resistor. R 19 This is the nineteenth resistor. R 20 The twentieth resistor, R 21 This is the twenty-first resistor. R 22 This is the twenty-second resistor. R 23 This is the twenty-third resistor. R 24 This is the twenty-fourth resistor. for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage.

[0028] According to the specific embodiments provided in this application, this application has the following technical effects: by realizing the synaptic connection between two neuron networks through memristors, it is possible to accurately simulate the synaptic transmission characteristics of biological neurons, improve the realism of biomimicry, successfully reproduce the chaotic dynamic behavior of biological neurons, efficiently generate hidden coexistence attractors, and enrich the dynamic performance of neuron systems. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of an isomorphic neuron system that generates a hidden coexistence attractor, provided as an embodiment of this application.

[0031] Figure 2 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0032] Figure 3 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0033] Figure 4 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0034] Figure 5 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0035] Figure 6 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0036] Figure 7 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0037] Figure 8 As shown in one embodiment of this application Circuit diagram of the branch circuit.

[0038] Figure 9 This is a circuit diagram of the tanh module in one embodiment of this application. Detailed Implementation

[0039] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0040] In neuromorphic computing, biological neurons exhibit a wealth of nonlinear phenomena, such as chaotic oscillations, multistable switching, and hidden attractors. These characteristics are crucial for achieving efficient neuromorphic computing. This application introduces memristors into neural networks as synaptic coupling elements. Memristors, the fourth basic electronic component besides resistors, capacitors, and inductors, possess memory and nonlinear dynamic characteristics, effectively simulating the plasticity of biological synapses and enhancing the dynamic behavior regulation capabilities of neural networks. The isomorphic neural network circuit provided in this application can be applied to fields such as neuromorphic computing, intelligent information processing, secure communication, and brain-computer interfaces.

[0041] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] In one exemplary embodiment, such as Figure 1 As shown, an isomorphic neuron system for generating hidden coexistence attractors is provided, including: a memristor 101, a first neuron network 102, and a second neuron network 103. The first neuron network 102 and the second neuron network 103 have the same structure.

[0043] The first neural network 102 and the second neural network 103 are synaptactically connected through the memristor 101 to simulate the chaotic dynamics of biological neurons and generate a hidden coexistence attractor.

[0044] This application proposes an isomorphic neuronal network composed of two identical three-dimensional HNNs, with synaptic connections achieved through memristors 101 to characterize the coupling behavior of homoproton networks within functional regions. The isomorphic neuronal system possesses characteristics such as periodicity, continuous differentiability, and nonlinearity, enabling it to simulate the dynamic plasticity and historical dependence exhibited by biological synapses during signal transmission, thereby enhancing the network's adaptability and learning ability, and realizing the generation of hidden coexistence attractors. By regulating the coupling strength of some neurons between networks, the system's dynamic behavior exhibits significant differences with parameter variations. The modular approach improves the accuracy of hardware simulation, providing a new technical solution for the development of brain-like intelligent hardware.

[0045] In a specific application example, neurons are connected via synapses, which ensure communication between neurons. Because the memristor 101 can mimic the plasticity of biological synapses, it can realistically update synaptic weights in real time in response to external stimuli. Therefore, this application employs an ideal flux-controlled memristor with cosine reactance, the expression of which is:

[0046] ;

[0047] in, i For current, v For voltage, For the sake of memory, For magnetic flux, for The first derivative, For state variables, .

[0048] Both the first neural network 102 and the second neural network 103 are three-dimensional Hopfield Neural Networks (HNNs), and their expressions are as follows:

[0049] ;

[0050] in, x k For neurons k membrane potential, x j For neurons j membrane potential, C k For neurons k Capacitance inside and outside the cell, R k For neurons k Membrane resistance inside and outside the cell, n For the number of neurons, w kj For neurons k With neuronsj Synaptic weights, determined by neurons k With neurons j The strength of the connection between them determines, I k For neurons k The input bias current is typically set to zero, and the hyperbolic tangent function is used. As an activation function 。

[0051] Both the first neuron network 102 and the second neuron network 103 include 3 neurons. The mathematical equation of the isomorphic neuron system is:

[0052] ;

[0053] in, This represents the membrane potential of the first neuron in the first neuron network 102. This represents the membrane potential of the second neuron in the first neuronal network 102. This represents the membrane potential of the third neuron in the first neuron network 102. This represents the membrane potential of the first neuron in the second neuronal network 103. This represents the membrane potential of the second neuron in the second neuron network 103. This represents the membrane potential of the third neuron in the second neuron network 103. For magnetic flux, t Let g1 be the self-coupling strength of the first neuron in the first neuron network 102 and the second neuron network 103, g2 be the coupling strength between the second neuron and the first neuron in the first neuron network 102 and the second neuron network 103, and g3 be the coupling strength between the third neuron and the first neuron in the first neuron network 102 and the second neuron network 103. When g3=0, the coupling strength between some neurons at the same location in the isomorphic neuron system changes synchronously.

[0054] From the above mathematical equations, it can be concluded that, R k and C k Both are 1. I k When = 0, it is a standard 3D HNN model, meaning the first equation does not include = 0. Item. Since this application uses a homogeneous HNN model, equations four through six are identical to the first three equations, except that equation four does not include... The first three equations represent the first neural network 102, the fourth to sixth equations represent the second neural network 103, and the last equation represents the state variables of the memristor 101. The memristor 101 connects the first neuron of the first neural network 102 and the first neuron of the second neural network 103. Mathematically, this is represented by adding coupling terms to the state variable expressions of the first neuron of the first neural network 102 and the first neuron of the second neural network 103. That is, addition and subtraction in the first and fourth equations. This indicates that the two neurons are connected by memristor 101 as a synapse.

[0055] The mathematical equations of the isomorphic neuron system provided in this application are implemented based on capacitors, resistors, operational amplifiers, analog multipliers, and function generators. The reciprocal function is implemented by connecting analog multipliers, and the core module of the isomorphic neuron network circuit is constructed using operational amplifiers and analog multipliers. The core of the sinusoidal memristor function is implemented by the function generator. Hidden multistable excitation is achieved by setting the initial voltage of the capacitor, and dynamic adjustment of system parameters is achieved through a combination of potentiometers and voltage sources, facilitating experimental research and engineering applications. Following the modular circuit design concept, the implementation complexity of the memristor-coupled isomorphic neuron system is reduced, and the system's scalability is enhanced, possessing significant theoretical research and engineering application value.

[0056] Among them, capacitors and resistors are used to control the values ​​of g1, g2 and g3, thereby adjusting the attractor; operational amplifiers are used to perform integration operations; analog multipliers are used to perform nonlinear operations; and function generators are used to perform trigonometric function operations.

[0057] The circuit for implementing the mathematical equations of the isomorphic neuron system includes Side roads Side roads Side roads Side roads Side roads branch roads and Branches. Each branch includes capacitors, resistors, operational amplifiers, analog multipliers, and function generators. To ensure a clear and intuitive representation of the circuit structure, the branches are connected using network tags, i.e. Figures 2 to 8 The fact that the output and input of the middle branch are the same indicates that they are connected, making the input and output of each branch intuitively visible. The coupling between each branch is strictly connected according to the circuit equation obtained by combining the corresponding dimensionless equation with Kirchhoff's laws and then dimensionalizing it. Excluding the tanh module, it consists of 38 resistors, 7 capacitors, 7 operational amplifiers, and 2 analog multipliers. The entire equivalent circuit is driven by a dual 12V DC power supply.

[0058] System initial value The value is set to (1,1,1,1,1,1,1,1). The absolute value function circuit is implemented by connecting the sign function circuit and the multiplier circuit. The operational amplifier is a TL082CD with a power supply voltage of ±15V and a normal saturation voltage of ±13.5V. The analog multiplier is an AD633JN with a power supply voltage of ±15V and a normal saturation voltage of ±10V. The function generator is an AD639AD with a power supply voltage of ±15V and a normal saturation voltage of ±10V. The standard design of the tanh module is as follows: Figure 9 As shown, it consists of three parts: an input buffer, a transistor core, and a differential operational amplifier output. After the signal is converted from voltage to current, a differential tanh current is generated by a complementary transistor, and finally, the operational amplifier converts it into a single-ended voltage output. The input voltage is ±15V.

[0059] The circuit equation for the branch is:

[0060] ;

[0061] like Figure 2 As shown, The first capacitor in the branch C 1. First resistor R 1. Second resistor R 2. Third resistor R 3. Fourth resistor R 4 is connected to the negative input of the operational amplifier, and the analog multiplier representing the neural network coupling term is connected via the fourth resistor. R 4 is connected to an operational amplifier, the positive input terminal of which is grounded, and the output is... x 1a Then it enters the tanh module and outputs... V tanh( x 1a The output terminal is connected to an inverter, and the output is - V tanh( x 1a Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, analyzing the connection point of the negative input terminal of the operational amplifier verifies the correspondence between the above circuit equations and the first equation in the mathematical equations of the isomorphic neuron system.

[0062] The circuit equation for the branch is:

[0063] ;

[0064] like Figure 3 As shown, The second capacitor in the branchC 2. Fifth resistor R 5. Sixth resistor R 6. The seventh resistor R 7. The eighth resistor R 8 is connected to the negative input terminal of the operational amplifier, and the positive input terminal of the operational amplifier is grounded. The output is... x 2a Then it enters the tanh module and outputs... V tanh( x 2a The output terminal is connected to an inverter, and the output is - V tanh( x 2a Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, by analyzing the connection point of the negative input terminal of the operational amplifier, the correspondence between the above circuit equation and the second equation in the mathematical equation of the isomorphic neuron system can be verified.

[0065] The circuit equation for the branch is:

[0066] ;

[0067] like Figure 4 As shown, The third capacitor in the branch C 3. Ninth resistor R 9. Tenth resistor R 10 Eleventh resistor R 11 Connect the negative input terminal of the operational amplifier to ground, and the positive input terminal of the operational amplifier is grounded. The output is... x 3a Then it enters the tanh module and outputs... V tanh( x 3a The output terminal is connected to an inverter, and the output is - V tanh( x 3a Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, by analyzing the connection point of the negative input terminal of the operational amplifier, the correspondence between the above circuit equations and the third equation in the mathematical equations of the isomorphic neuron system can be verified.

[0068] The circuit equation for the branch is:

[0069] ;

[0070] like Figure 5 As shown, The fourth capacitor in the branchC 4. The twelfth resistor R 12 Thirteenth resistor R 13 Fourteenth resistor R 14 The fifteenth resistor R 15 Connected to the negative input of the operational amplifier, the analog multiplier representing the neural network coupling term is connected via the fifteenth resistor. R 15 Connected to an operational amplifier, with the positive input terminal of the operational amplifier grounded, the output is... x 1b Then it enters the tanh module and outputs... V tanh( x 1b The output terminal is connected to an inverter, and the output is - V tanh( x 1b Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, by analyzing the connection point of the negative input terminal of the operational amplifier, the correspondence between the above circuit equations and the fourth equation in the mathematical equations of the isomorphic neuron system can be verified.

[0071] The circuit equation for the branch is:

[0072] ;

[0073] like Figure 6 As shown, The fifth capacitor in the branch C 5. Sixteenth resistor R 16 Seventeenth resistor R 17 The eighteenth resistor 、 Nineteenth resistor R 19 Connect the negative input terminal of the operational amplifier to ground, and the positive input terminal of the operational amplifier is grounded. The output is... x 2b Then it enters the tanh module and outputs... V tanh( x 2b The output terminal is connected to an inverter, and the output is - V tanh( x 2b Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, by analyzing the connection point of the negative input terminal of the operational amplifier, the correspondence between the above circuit equations and the fifth equation in the mathematical equations of the isomorphic neuron system can be verified.

[0074] The circuit equation for the branch is:

[0075] ;

[0076] like Figure 7 As shown, The sixth capacitor in the branch C 6. The twentieth resistor R 20 21st resistor R 21 22nd resistor R 22 Connect the operational amplifier to its negative input terminal, and ground the positive input terminal of the operational amplifier. The output is... x 3b Then it enters the tanh module and outputs... V tanh( x 3b The output terminal is connected to an inverter, and the output is - V tanh( x 3b Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, analyzing the connection point of the negative input terminal of the operational amplifier verifies the correspondence between the above circuit equations and the sixth equation in the mathematical equations of the isomorphic neuron system.

[0077] The circuit equation for the branch is:

[0078] ;

[0079] like Figure 8 As shown, The seventh capacitor in the branch C 7. The twenty-third resistor R 23 24th resistor R 24 Connect the negative input terminal of the operational amplifier to ground, and the positive input terminal of the operational amplifier is grounded. The output is... The output is connected to the AD639, and the output is... V cos( Connect an inverter, the output is - V cos( Based on Kirchhoff's current law and the virtual short and virtual open characteristics of operational amplifiers, analyzing the connection point of the negative input terminal of the operational amplifier verifies the correspondence between the above circuit equations and the seventh equation in the mathematical equations of the isomorphic neuron system.

[0080] In the circuit equations of the above branches, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage.

[0081] Let the time integration constant RC =0.1ms, take R =10kΩ, C =10nF. By comparing Kirchhoff's equations with the mathematical equations of isomorphic neuron systems, the corresponding component parameters of the circuit can be calculated using the parameters of the corresponding HNN. C = C 1= C 2= C 3= C 4= C 5= C 6= C 7 = 10nF R =10kΩ. Capacitor. C 1- C The voltage of 7 represents the state variable of the neuronal system. x 1a - The resistance value corresponds to the coupling weight, and its resistance value is equal to " R / Coupling weight w kj ". Calculations show that R 1= R 12 = R 5= R 16 = R 9=R 20 = R 4= R 13 =10kΩ, R 3= R 14 =5.556kΩ, R 7= R 18 =9.091kΩ, R 8= R 19 =7.69kΩ, R 10 = R 21 =3.33kΩ, R 11 = R 22 =6.66kΩ, R 23 = R 24 =5.88kΩ, R 2 and R 15 Subject to parameters g 1. Regulation, R 6 and R 17 Subject to parameters g 2. Regulation. When g 1 = 1.16 g When 2=2.4, R 2= R 13 =9.09kΩ, R 6= R 17 =4.166kΩ. Simulation verification was performed using PSpice, followed by hardware circuit implementation and experimentation. The results obtained were consistent with the numerical simulation, proving the feasibility of the proposed solution.

[0082] In summary, this circuit achieves the circuit design of memristor-coupled isomorphic neural networks with fewer active components. In practical applications, it exhibits richer dynamic characteristics while consuming fewer resources, thus improving the stability of the entire circuit and system.

[0083] Current neuronal systems are mainly composed of single neurons, with relatively simple structures and dynamic characteristics. HNNs are simplified neural network models whose structure is very similar to that of the neural network in the biological brain, and whose dynamic behavior matches certain behavioral characteristics of neuronal networks in the brain. The memristor-coupled isomorphic neuronal system proposed in this application has better biomimicry. By realizing synaptic connections through memristors to characterize the coupling behavior of homoproton networks within functional regions, it can generate richer dynamic behaviors and more complex chaotic attractors. Compared with traditional schemes, the introduction of memristor-coupled isomorphic neural networks not only enhances the nonlinearity of the neuronal system but also significantly increases the complexity of chaotic signals.

[0084] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0086] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. An isomorphic neuron system for generating hidden coexistence attractors, characterized in that, The isomorphic neuron system includes: a memristor, a first neuron network, and a second neuron network; the first neuron network and the second neuron network have the same structure; the memristor is an ideal flux-controlled memristor with cosine reactance. The first neuron network and the second neuron network are synaptic connected through the memristor to simulate the chaotic dynamics of biological neurons and generate a hidden coexistence attractor. Both the first neural network and the second neural network include 3 neurons; The mathematical equations of the isomorphic neuron system are: ； in, This represents the membrane potential of the first neuron in the first neuron network. This represents the membrane potential of the second neuron in the first neuronal network. This represents the membrane potential of the third neuron in the first neuron network. This represents the membrane potential of the first neuron in the second neuronal network. This represents the membrane potential of the second neuron in the second neuron network. This represents the membrane potential of the third neuron in the second neuronal network. For magnetic flux, t Let g be time, g1 be the self-coupling strength of the first neuron in the first neuron network and the second neuron network, g2 be the coupling strength between the second neuron and the first neuron in the first neuron network and the second neuron network, and g3 be the coupling strength between the third neuron and the first neuron in the first neuron network and the second neuron network.

2. The isomorphic neuron system for generating hidden coexistence attractors according to claim 1, characterized in that, The expression for the ideal flux-controlled memristor with cosine reactance is: ； in, i For current, v For voltage, For the sake of memory, For magnetic flux, for The first derivative, It is a state variable.

3. The isomorphic neuron system for generating hidden coexistence attractors according to claim 1, characterized in that, Both the first and second neuron networks are three-dimensional Hopfield neural networks.

4. The isomorphic neuron system for generating hidden coexistence attractors according to claim 1, characterized in that, The expressions for the first neural network and the second neural network are as follows: ； in, x k For neurons k membrane potential, x j For neurons j membrane potential, C k For neurons k Capacitance inside and outside the cell, R k For neurons k Membrane resistance inside and outside the cell, n For the number of neurons, w kj For neurons k With neurons j Synaptic weights, determined by neurons k With neurons j The strength of the connection between them determines, I k For neurons k Input bias current 。 5. The isomorphic neuron system for generating hidden coexistence attractors according to claim 1, characterized in that, The mathematical equations of the isomorphic neuron system are implemented based on capacitors, resistors, operational amplifiers, analog multipliers, and function generators; Among them, capacitors and resistors are used to control the values ​​of g1, g2 and g3, operational amplifiers are used to perform integration operations, analog multipliers are used to perform nonlinear operations, and function generators are used to perform trigonometric function operations.

6. The isomorphic neuron system for generating hidden coexistence attractors according to claim 5, characterized in that, The circuit for implementing the mathematical equations of the isomorphic neuron system includes Side roads Side roads Side roads Side roads Side roads branch roads and Branch circuits; each branch circuit includes capacitors, resistors, operational amplifiers, analog multipliers, and function generators.

7. The isomorphic neuron system for generating hidden coexistence attractors according to claim 6, characterized in that, The circuit equation for the branch is: ； The circuit equation for the branch is: ； The circuit equation for the branch is: ； The circuit equation for the branch is: ； The circuit equation for the branch is: ； The circuit equation for the branch is: ； The circuit equation for the branch is: ； in, C 1 is the first capacitor. C 2 is the second capacitor. C 3 is the third capacitor. C 4 is the fourth capacitor. C 5 is the fifth capacitor. C 6 is the sixth capacitor. C 7 is the seventh capacitor. R 1 represents the first resistor. R 2 is the second resistor. R 3 is the third resistor. R 4 is the fourth resistor. R 5 is the fifth resistor. R 6 is the sixth resistor. R 7 is the seventh resistor. R 8 represents the eighth resistor. R 9 is the ninth resistor. R 10 The tenth resistor, R 11 The eleventh resistor, R 12 The twelfth resistor, R 13 It is the thirteenth resistor. R 14 This is the fourteenth resistor. R 15 This is the fifteenth resistor. R 16 This is the sixteenth resistor. R 17 This is the seventeenth resistor. R 18 This is the eighteenth resistor. R 19 This is the nineteenth resistor. R 20 The twentieth resistor, R 21 The twenty-first resistor, R 22 This is the twenty-second resistor. R 23 This is the twenty-third resistor. R 24 This is the twenty-fourth resistor. for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage, for The corresponding voltage.

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