A multi-scroll chaotic circuit

Abstract

The application belongs to the technical field of electronic circuit technology and discloses a multi-scroll chaotic circuit, wherein three integral circuits are arranged, each integral circuit is linearly connected with a summer circuit, the summer circuit is provided with two kinds, namely, a multiplier summer circuit and a controlled voltage source circuit, each integral circuit is connected with each other, and the integral circuits are sequentially arranged from top to bottom as a first integral circuit, a second integral circuit and a third integral circuit. The first integral circuit is provided with a voltage source VS1, the anode of the voltage source VS1 is connected with one end of R8, the reverse input end of summer U3 and one end of R6 through R7, the other end of R6 is connected with the output end of K1, the output end of summer U3 is connected with the other end of R8, the input end of K7, the input end of K4 and one input end of M3. By adjusting the controlled voltage source Vs1, the obtained two scroll can be folded to the x-axis direction, four scroll are generated, and by changing the size of Vs1, six scroll can be generated.

Description

Technical Field

[0001] This invention belongs to the field of electronic circuit technology, and in particular relates to a multi-vortex chaotic circuit. Background Technology

[0002] In the early 1990s, based on the normalized equations of Chua's circuit, Suykens and Vandewalle discovered multi-vortex chaotic attractors by introducing inflection points in nonlinear function curves. Compared to traditional single-vortex and double-vortex chaotic systems, multi-vortex chaotic systems exhibit more complex mechanical behavior and show considerable promise for applications in secure communication and information hiding. Therefore, multi-vortex chaotic circuits have become a research hotspot in the field of chaos.

[0003] Existing technologies modify low-dimensional chaotic systems by employing different piecewise linear or nonlinear functions in order to obtain equilibrium points where the root of the system's eigenvalues ​​is exponential 2. Based on the Chua circuit, Yalcin, Lü Jinhu, and Yu Simin et al. achieved the generation of multi-vortex chaotic attractors in one-dimensional, two-dimensional, and three-dimensional spaces by loading different multi-turn-point piecewise linear functions for driving.

[0004] Based on the double-vortex chaotic system, by constructing various nonlinear functions, the saddle-fossil equilibrium point in the original double-vortex chaotic system can be extended. If a nonlinear function is constructed, the saddle-fossil equilibrium point of index 2 can be extended in a certain direction. If two nonlinear functions are constructed, the saddle-fossil equilibrium point of index 2 can be extended in two directions at the same time. If multiple nonlinear functions are constructed, the saddle-fossil equilibrium point of index 2 can be extended in multiple directions at the same time. This is called a multi-directional distributed multi-dimensional grid-like multi-vortex system.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows: it is difficult for the existing technology to achieve adjustment and control of multi-directional distributed multi-dimensional grid-like multi-vortex systems. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a multi-vortex chaotic circuit.

[0007] This invention is implemented as follows: a multi-vortex chaotic circuit includes:

[0008] Integrating circuit;

[0009] There are three integrator circuits, each linearly connected to an adder circuit. There are two types of adder circuits: a multiplier adder circuit and a controlled voltage source circuit. The integrator circuits are interconnected, and from top to bottom, they are the first integrator circuit, the second integrator circuit, and the third integrator circuit. The integrator circuits are based on the charging and discharging principle of a capacitor, and can achieve delay, timing, and the generation of various waveforms during the charging and discharging process.

[0010] Furthermore, the first integrating circuit is provided with a voltage source VS1. The positive terminal of the voltage source VS1 is connected to one end of R8, the inverting input terminal of adder U3 and one end of R6 through R7. The other end of R6 is connected to the output terminal of K1. The output terminal of adder U3 and the other end of R8 are connected to the input terminals of K7, K4 and M3.

[0011] Furthermore, the output of K4 is connected to one end of R4, one end of R2, one end of R3 and the inverting input of adder U2 via R5. The other end of R4 is connected to the output of K3, the other end of R3 is connected to the output of K2, and the other end of R2 is connected to the output of adder U2 and one end of R1.

[0012] Furthermore, the other end of R1 is connected to one end of C1 and the inverting input of the inverting amplifier U1, and the output of the inverting amplifier U1, the other end of C1, and the input of K1 are connected as the x-direction output of the chaotic circuit.

[0013] Furthermore, the second integrating circuit is provided with a third power supply VS2. The positive terminal of the third voltage source VS2 is connected to one end of R20, one end of R18 and the inverting input terminal of adder U8 after passing through R19. The output terminal of adder U8 is connected to the other end of R20 and the input terminal of K8, one input terminal of M2 and one input terminal of M1. The other end of R18 is connected to the output terminal of K10.

[0014] Furthermore, the output of M2 is connected to the inverting input of adder U5, one end of R12, one end of R10, and one end of R13 via K5 and R11 respectively. The other end of R13 is connected to the output of K7, the other end of R12 is connected to the output of K6, and the other end of R10 is connected to the output of adder U5 and one end of R9.

[0015] Furthermore, the third integrator circuit includes R9, one end of which is connected to one end of C2 and the inverting input terminal of the inverting amplifier U4. The output terminal of the inverting amplifier U4, the other end of C2, the input terminal of K3, the other input terminal of M1, the input terminal of K6, the other input terminal of M2, and the other input terminal of M3 are connected as the y-direction output terminal of the chaotic circuit.

[0016] Furthermore, the output of M3 is connected to one end of R15 and one end of R16 of adder U7 via K9 and R17. The other end of R16 is connected to the output of K8, and the other end of R15 is connected to the output of adder U7 and one end of R14.

[0017] Furthermore, the other end of R14 is connected to one end of C3 and the inverting input of the inverting amplifier U6, and the output of the inverting amplifier U6, the other end of C3, and the input of K10 are connected as the z-direction output of the chaotic circuit.

[0018] Furthermore, the non-inverting input terminals of the inverting amplifier U1, U4, U6, U2, U3, U5, U7, and U8, as well as the negative terminals of voltage sources VS1 and VS2, are all grounded.

[0019] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0020] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0021] This invention, based on the double-vortex chaotic system, expands the saddle-fossil equilibrium point of the original double-vortex chaotic system by constructing various nonlinear functions, forming a multi-vortex chaotic system. Compared with traditional single-vortex and double-vortex chaotic systems, the multi-vortex chaotic system exhibits more complex mechanical behavior. This invention enables the adjustment and control of a multi-directionally distributed, multi-dimensional grid-like multi-vortex system. This invention can be achieved by adjusting capacitors C1, C2, and C3 and resistors R1, R9, and R... 14 The size of the time constant and the amplification factor k can be changed to obtain two stable vortices in the system. By adjusting the controlled voltage source Vs1, the two vortices can be folded in the x-axis direction to produce four vortices. By changing the size of Vs1, six vortices can be produced.

[0022] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0023] Based on the system's state equations, this invention allows for the construction of experimental simulation circuits. While keeping Vs1 constant, changing another controlled voltage source, Vs2, can fold the image in the z-direction, forming four, eight, or twelve vortices. This invention enriches the theory of multi-vortex chaos and promotes its application in science and engineering. Furthermore, this invention proposes a multi-vortex chaotic circuit that can be applied to secure communication, gradually replacing low-dimensional chaotic encryption mechanisms.

[0024] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0025] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0026] Compared to traditional dual-vortex chaotic systems, multi-vortex chaotic systems possess more key parameters. This means that numerous vortices can exhibit a planar or three-dimensional grid structure distributed in one or even multiple directions in phase space, with nested topologies among them. The number of vortices and their grid-like distribution are determined by the system parameters. Furthermore, multi-vortex chaotic circuits exhibit more complex dynamic characteristics. This complexity manifests in the ability of the state variables or phase trajectories of the chaotic attractors to jump between multiple different vortices. Therefore, the greater the number of vortices, the greater this randomness, making it more advantageous for information encryption.

[0027] (2) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0028] This invention can be applied to chaotic secure communication. Compared with traditional double-vortex chaotic attractors, multi-vortex chaotic attractors have more complex dynamic characteristics and more key parameters, giving them superior security performance in chaotic secure communication and broader application prospects. Constructing high-performance multi-vortex chaotic systems has significant practical implications. This invention addresses the limitations of generating a limited number of multi-vortex chaotic attractors in practical circuit implementations, as well as the shortcomings of generating multi-vortex chaotic attractors in practical chaotic circuits, which are often unidirectional and limited in number. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a multi-vortex chaotic circuit provided in an embodiment of the present invention;

[0030] Figure 2 This is a V-shaped pattern with two spirals formed in the xz plane, as provided in an embodiment of the present invention.

[0031] Figure 3 The expression for adjusting the controlled voltage source Vs1 provided in this embodiment of the invention is 1.2*(sign(x)), which results in two “V”-shaped and four spiral diagrams formed in the xz plane.

[0032] Figure 4 The embodiment of the present invention provides a diagram of 3 “V” shapes and 6 spirals formed in the xz plane when the expression of Vs1 is adjusted to 1.2*(sign(x))+0.55*(sign(x+1.2))+0.55*(sign(x-1.2)).

[0033] Figure 5 The embodiment of the present invention provides a V-shaped pattern of four spirals formed in the xz plane when the expression of Vs1 is 0 and the expression of the controlled voltage source Vs2 is adjusted to 2*(sign(z-3)).

[0034] Figure 6 This invention provides a method for creating two "V"-shaped 8-vortex diagrams in the xz plane when the expression of Vs1 is 1.2*(sign(x)) and the expression of Vs2 is adjusted to 2*(sign(z-3)).

[0035] Figure 7 When the expression of Vs1 provided in this embodiment of the invention is 1.2*(sign(x))+0.55*(sign(x+1.2))+0.55*(sign(x-1.2)), and the size of the controlled voltage source Vs2 is adjusted to 2*(sign(z-3)), 3 "V" shaped 12 spiral diagrams are formed in the xz plane. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory description of the embodiments that expand upon the technical solutions of the claims.

[0038] like Figures 1-7 As shown, the multi-vortex chaotic circuit provided in this embodiment of the invention has three integrator circuits. Each integrator circuit is linearly connected to an adder circuit. There are two types of adder circuits: a multiplier adder circuit and a controlled voltage source circuit. Each integrator circuit is interconnected. From top to bottom, the integrator circuits are the first integrator circuit, the second integrator circuit, and the third integrator circuit.

[0039] The first integrating circuit has a voltage source VS1. The positive terminal of the voltage source VS1 is connected to one end of R8, the inverting input terminal of adder U3, and one end of R6 through R7. The other end of R6 is connected to the output terminal of K1. The output terminal of adder U3 and the other end of R8 are connected to the input terminals of K7, K4, and one input terminal of M3.

[0040] The output of K4 is connected to one end of R4, one end of R2, one end of R3 and the inverting input of adder U2 via R5. The other end of R4 is connected to the output of K3, the other end of R3 is connected to the output of K2, and the other end of R2 is connected to the output of adder U2 and one end of R1.

[0041] The other end of R1 is connected to one end of C1 and the inverting input of the inverting amplifier U1. The output of the inverting amplifier U1, the other end of C1, and the input of K1 are connected as the x-direction output of the chaotic circuit.

[0042] The second integrating circuit has a third power supply VS2. The positive terminal of the third voltage source VS2 is connected to one end of R20, one end of R18 and the inverting input terminal of adder U8 after passing through R19. The output terminal of adder U8 is connected to the other end of R20 and the input terminal of K8, one input terminal of M2 and one input terminal of M1. The other end of R18 is connected to the output terminal of K10.

[0043] The output of M2 is connected to the inverting input of adder U5, one end of R12, one end of R10, and one end of R13 via K5 and R11 respectively. The other end of R13 is connected to the output of K7, the other end of R12 is connected to the output of K6, and the other end of R10 is connected to the output of adder U5 and one end of R9.

[0044] The third integrator circuit has R9. One end of R9 is connected to one end of C2 and the inverting input of the inverting amplifier U4. The output of the inverting amplifier U4, the other end of C2, the input of K3, the other input of M1, the input of K6, the other input of M2, and the other input of M3 are connected to serve as the y-direction output of the chaotic circuit.

[0045] The output of M3 is connected to one end of R15 and one end of R16 after passing through K9 and R17. The other end of R16 is connected to the output of K8, and the other end of R15 is connected to the output of adder U7 and one end of R14.

[0046] The other end of R14 is connected to one end of C3 and the inverting input of the inverting amplifier U6. The output of the inverting amplifier U6, the other end of C3, and the input of K10 are connected as the z-direction output of the chaotic circuit.

[0047] The non-inverting input terminals of inverting amplifier U1, inverting amplifier U4, inverting amplifier U6, adder U2, adder U3, adder U5, adder U7, adder U8, the negative terminal of voltage source VS1, and the negative terminal of voltage source VS2 are all grounded.

[0048] The state equation of a V-shaped multi-scroll circuit system is:

[0049]

[0050] in: a = 10, b = 45, c = 0.0126, d = 8 / 3. From the state equation (1), the equilibrium point of the system can be obtained as:

[0051]

[0052] The Jacobian matrix of the system at the equilibrium point is:

[0053]

[0054] When parameters a1 = a2 = b = 0, the system's equilibrium point x variables are -0.655, 0.655, 0. The eigenvalues ​​of the Jacobian matrix at equilibrium point 0 are -122.7, -26.67, 12.75. At this point, the equilibrium point is an unstable saddle point. The eigenvalues ​​of the Jacobian matrix at the two non-zero equilibrium points are -142, 2.6569+75.58i, 2.6569-75.58i. At these two points, the equilibrium points are unstable saddle foci. Therefore, the system will form a "V"-shaped two-vortex at this time, as shown below. Figure 2 As shown, by adjusting the parameters a1, a2, and b, the number of unstable saddle points and saddle focal points can be controlled, thereby controlling the number of "V" shapes and the number of vortices.

[0055] To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides specific product or related technology application examples of the technical solution claimed.

[0056] This invention utilizes the characteristic of multi-vortex chaotic systems that can generate numerous vortices in phase space to encrypt a single channel of information. Then, according to a certain method, the information signal is encrypted into different vortices at different times. Therefore, the research on multi-vortex chaotic circuits not only has special application value in the field of chaos science research, but also has high development prospects in multi-channel information encryption.

[0057] This invention utilizes a multi-vortex chaotic system to achieve secure transmission of binary digital signals. The multi-vortex chaotic signal exhibits superior randomness due to the random jumping between multiple vortices. Furthermore, the multi-vortex chaotic system can achieve modulation of multiple parameters, providing multiple key parameters. Even within the same chaotic system, minute changes in parameter values ​​can produce drastically different results. Therefore, using a multi-vortex system for secure communication offers superior security performance and is more difficult for enemy agents to decipher, showing broad application prospects in both military communications and civilian information security.

[0058] The embodiments of the present invention have achieved some positive results during the research and development or use process, and have indeed great advantages compared with the prior art. The following content describes them in conjunction with the data, charts and other information of the experimental process.

[0059] Based on the system's state equations, experimental simulation circuits can be built, such as... Figure 1 As shown, the entire system mainly consists of an operational amplifier, a multiplier, resistors, capacitors, and a controlled source. The selected resistors are 100KΩ, the capacitors are 10µF, the operational amplifier is a TL082, and to improve waveform accuracy, all resistors are 1% color-coded resistors; film capacitors are used.

[0060] according to Figure 1 The circuit shown connects the various components, and the relevant circuit parameters are determined. Due to unavoidable errors between theoretical simulation and actual circuit, the circuit parameters will have some discrepancies with the theoretical values ​​during actual hardware circuit experiments. By fine-tuning the values ​​of capacitors C1, C2, and C3, changing the time constant of the integrator, and simultaneously fine-tuning the feedback factor accordingly, the parameters required for the actual hardware circuit can be obtained.

[0061] In the feedback loop of x and z, the parameters of the controlled source are controlled according to the expressions f(x) and f(z) above, and the circuit is... Figure 1 Input the x and z variables into the oscilloscope and adjust the oscilloscope to xy phase test mode. After 1-2 minutes, you can observe the results on the oscilloscope. Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 The multi-vortex phase diagram shown.

[0062] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A multi-scroll chaotic circuit, characterized by, The multi-scroll chaotic circuit is provided with: an integration circuit; The integration circuit is provided with three, each of which is linearly connected with a summer circuit, the summer circuit is provided with two types, which are a multiplier summer circuit and a controlled voltage source circuit, each of the integration circuits is connected with each other, and the integration circuits from top to bottom are a first integration circuit, a second integration circuit and a third integration circuit; The first integration circuit is provided with a voltage source VS1, the anode of the voltage source VS1 is connected with one end of R8, the reverse input end of summer U3 and one end of R6 through R7, the other end of R6 is connected with the output end of K1, the output end of summer U3 is connected with the other end of R8, the input end of K7, the input end of K4 and one input end of M3; The output end of K4 is connected with one end of R4, one end of R2, one end of R3 and the reverse input end of summer U2 through R5, the other end of R4 is connected with the output end of K3, the other end of R3 is connected with the output end of K2, the other end of R2 is connected with the output end of summer U2 and one end of R1.

2. The multi-scroll chaotic circuit of claim 1, wherein, The other end of R1 is connected with one end of C1 and the reverse input end of reverse amplifier U1, the output end of reverse amplifier U1, the other end of C1 and the input end of K1 are connected as the x-direction output end of the chaotic circuit.

3. The multi-scroll chaotic circuit of claim 1, wherein The second integration circuit is provided with a third voltage source VS2, the anode of the third voltage source VS2 is connected with one end of R20, one end of R18 and the reverse input end of summer U8 through R19, the output end of summer U8 is connected with the other end of R20, the input end of K8, one input end of M2 and one input end of M1, the other end of R18 is connected with the output end of K10.

4. The multi-scroll chaotic circuit of claim 3, wherein, The output end of M2 is connected with the reverse input end of summer U5, one end of R12, one end of R10 and one end of R13 through K5 and R11, the other end of R13 is connected with the output end of K7, the other end of R12 is connected with the output end of K6, the other end of R10 is connected with the output end of summer U5 and one end of R9.

5. The multi-scroll chaotic circuit of claim 1, wherein, The third integration circuit is provided with R9, one end of R9 is connected with one end of C2 and the reverse input end of reverse amplifier U4, the output end of reverse amplifier U4, the other end of C2, the input end of K3, the other input end of M1, the input end of K6, the other input end of M2 and the other input end of M3 are connected as the y-direction output end of the chaotic circuit.

6. The multi-scroll chaotic circuit of claim 5, wherein, The output end of M3 is connected with one end of R15, one end of R16 and the reverse input end of summer U7 through K9 and R17, the other end of R16 is connected with the output end of K8, the other end of R15 is connected with the output end of summer U7 and one end of R14.

7. The multi-scroll chaotic circuit of claim 6, wherein, The other end of R14 is connected with one end of C3 and the reverse input end of reverse amplifier U6, the output end of reverse amplifier U6, the other end of C3 and the input end of K10 are connected as the z-direction output end of the chaotic circuit.

8. The multi-scroll chaotic circuit of claim 2, wherein, The noninverted input of the inverting amplifier U1, the noninverted input of the inverting amplifier U4, the noninverted input of the inverting amplifier U6, the noninverted input of the adder U2, the noninverted input of the adder U3, the noninverted input of the adder U5, the noninverted input of the adder U7, the noninverted input of the adder U8, the negative pole of the voltage source VS1 and the negative pole of the voltage source VS2 are all grounded.

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