Method and device for controlling divergence of single variable of memristor chaotic system along with time

Abstract

The invention discloses a method and device for controlling divergence of a single variable of a memristor chaotic system along with time, and relates to the technical field of electronic circuits, and the method comprises the steps: determining a basic chaotic system of a single-structure attractor, and the order of the basic chaotic system is not limited; expanding the basic chaotic system by using a universal initial enhanced memristor to construct a memristive chaotic system, wherein the memristive chaotic system can generate any number of chaotic attractors diverging along with time; the dimension is determined according to the divergence direction of the variable, and a constant term is introduced, so that the divergence of the variable is controlled. A memristor chaotic system is constructed by using an initial enhanced memristor according to a basic chaotic system, and divergence of a control variable is realized by introducing a constant quantity on the premise of not changing the dimension and complexity of the system. The method is suitable for a self-reproduction attractor memristor chaotic system, a single variable in the memristor chaotic system is controlled to diverge along with time, and the realization difficulty in a circuit is reduced.

Description

Technical Field

[0001] The present application relates to the field of electronic circuit technology, and in particular to a method and device for controlling the divergence of a single variable of a memristor chaotic system over time. Background Art

[0002] The multistability of dynamic systems is a hot topic in nonlinear science and engineering research. Bias control is also a newly discovered means of effective attractor divergence, which shows its strong dynamic control performance even in memristor systems. Li Chunbiao introduced a periodic trigonometric function based on the initial value to form a bias-enhanced periodic trigonometric function to realize the divergence and reproduction of attractors. He Shaobo introduced a periodic trigonometric function to obtain self-reproducing attractors, and analyzed the multi-scale multivariate permutation entropy based on the multi-scale multivariate complexity algorithm. Gu Jiacheng used a hyperbolic function-type magnetically controlled memristor to realize the unidirectional self-reproduction of attractors. Bao Han introduced an initial enhanced memristor to obtain a self-reproducing attractor and explained the actual discharge activity of biological neurons.

[0003] The above work has made a preliminary exploration of the self-propagating behavior of attractors. However, although these phenomena can be applied in communications and images, they are difficult to implement in actual circuits. Therefore, how to control the divergence of a single variable in a self-propagating memristor chaotic system over time and then control the boundary of the attractor to facilitate the implementation of actual circuits is an important research topic with application value. Summary of the invention

[0004] In order to solve the above technical problems, the following technical solutions are proposed:

[0005] In a first aspect, an embodiment of the present application provides a method for controlling the divergence of a single variable of a memristor chaotic system over time, comprising:

[0006] Determine a basic chaotic system of a single structural attractor, wherein the dimension of the basic chaotic system is not restricted;

[0007] The basic chaotic system is extended by using a universal initial enhanced memristor to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time;

[0008] The dimension is determined according to the direction in which the variable diverges and a constant term is introduced to control the divergence of the variable.

[0009] In a possible implementation, the determining of a basic chaotic system of a single structural attractor includes:

[0010] Select a basic chaotic system with a single structural attractor

[0011] Said Including basic chaotic system and neuron chaotic system, expressed as:

[0012]

[0013] Among them, x, y, z, u are the state variables of the chaotic system, and f1, f2, f3, f4 are the state equation expressions.

[0014] In a possible implementation, the initial enhanced memristor It is expressed as:

[0015]

[0016] g, h are the memristor parameters, m and e are the electromagnetic induction intensities, and φ is the internal state variable of the memristor.

[0017] In a possible implementation, the universal initial enhanced memristor expands the basic chaotic system to construct a memristor chaotic system, including:

[0018] Exploiting the initial enhancement of memristors For basic chaotic systems Expand and construct a memristor chaotic system The following formula is used to construct the memristor chaotic system:

[0019]

[0020] Where x, y, z, u, is the system state variable.

[0021] In one possible implementation, a memristor chaotic system By setting parameters, any number of chaotic attractors can be generated that diverge over time.

[0022] In a possible implementation, the dimension in which the variable is located is determined according to the direction in which the variable diverges and a constant term is introduced to control the divergence of the variable, including:

[0023] According to the direction of the variable divergence, a signed constant ±m is introduced into the dimension to control the divergence of the variable. Specifically, the following formula is used:

[0024]

[0025] In the formula, m is a newly introduced constant.

[0026] In a second aspect, an embodiment of the present application provides a device for controlling the divergence of a single variable of a memristor chaotic system over time, comprising:

[0027] A determination module, used for determining a basic chaotic system of a single structural attractor, wherein the dimension of the basic chaotic system is not restricted;

[0028] A construction module, used to expand the basic chaotic system by using a universal initial enhanced memristor to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time;

[0029] The divergence control module is used to determine the dimension according to the direction of the variable divergence and introduce a constant term to control the divergence of the variable.

[0030] In a third aspect, an embodiment of the present application provides an electronic circuit for implementing the method described in any possible implementation of the first aspect.

[0031] In a fourth aspect, an embodiment of the present application provides a computer storage medium, wherein the computer-readable storage medium includes a stored program, wherein when the program is running, the electronic device where the computer-readable storage medium is located is controlled to execute the method described in any possible implementation method of the first aspect.

[0032] In the embodiment of the present application, a memristor chaotic system is constructed based on the basic chaotic system using an initial enhanced memristor, and a constant is introduced to achieve the divergence of the control variable without changing the dimension and complexity of the system. It is applicable to the self-propagating attractor memristor chaotic system, and controls the divergence of a single variable in the memristor chaotic system over time, reducing the difficulty of implementation in the circuit. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A flow chart of a method for controlling the divergence of a single variable of a memristor chaotic system over time provided in an embodiment of the present application;

[0034] Figure 2 The divergent attractor phase diagram of the memristor chaotic system in different planes provided in the embodiment of the present application;

[0035] Figure 3 Phase diagrams of different planes after introducing constants provided in the embodiments of the present application;

[0036] Figure 4 A schematic diagram of a device for controlling the divergence of a single variable of a memristor chaotic system over time provided in an embodiment of the present application. DETAILED DESCRIPTION

[0037] The present solution is described below in conjunction with the accompanying drawings and specific implementation methods.

[0038] See also Figure 1 , the method for controlling the divergence of a single variable of a memristor chaotic system over time in this embodiment includes:

[0039] S101, determining a basic chaotic system of a single structural attractor, wherein the dimension of the basic chaotic system is not limited.

[0040] This example selects a basic chaotic system with a single structural attractor Said Including basic chaotic system and neuron chaotic system, expressed as:

[0041]

[0042] Among them, x, y, z, u are the state variables of the chaotic system, and f1, f2, f3, f4 are the state equation expressions.

[0043] S102, using a universal initial enhanced memristor to expand the basic chaotic system to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time.

[0044] According to the basic chaotic system selected above Using a universal initial enhancement memristor to study basic chaotic systems Expand and construct a memristor chaotic system Universal enhanced memristor It is expressed as:

[0045]

[0046] Where g, h are memristor parameters, m and e are electromagnetic induction strengths, is the internal state variable of the memristor.

[0047] Constructing a memristive chaotic system Memristor Chaotic System By setting parameters, any number of self-propagating chaotic attractors that diverge over time can be generated. The following formula is used to construct the memristor chaotic system:

[0048]

[0049] Where x, y, z, u, is the system state variable.

[0050] S103, determining the dimension according to the direction in which the variable diverges and introducing a constant term, thereby controlling the divergence of the variable.

[0051] (1) According to the direction in which the variable diverges from the self-propagating attractor, a signed constant (±m) is introduced in this dimension to control the divergence of the variable.

[0052] The specific formula used is as follows.

[0053]

[0054] In the formula, m is a newly introduced constant.

[0055] The effectiveness of this method is demonstrated below by generating self-reproducing attractors and inhibiting the generation of multiple attractors in a memristor chaotic system.

[0056] Control multiple attractors. The specific methods are as follows:

[0057] (1) The local active memristor with chaotic attractor is selected as the connection line between the coupling HR neuron and HNN neuron, and its system equation is:

[0058]

[0059] Wherein, parameters a=c=1, b=3, d=5, n=0.5, l=8, and k are adjustable parameters.

[0060] Using a universal initial enhancement memristor to study basic chaotic systems Expand and construct a memristor chaotic system

[0061]

[0062] In the formula, parameters a=c=1, b=3, d=5, n=0.5, l=8, e=0.5, and k is an adjustable parameter.

[0063]

[0064] In the formula, the parameters are m = 1, e = 0.5, g = 0.1, h = 1.25, and the initial value of the system is (1, 0, 0, -1, 1).

[0065] According to the direction in which the variable diverges with the self-propagating attractor, a signed constant (±m) is introduced in the dimension to control the divergence of the variable.

[0066]

[0067] Wherein, m=0.07.

[0068] Memristor Neural Network System Set the coupling parameter k. Figure 2 (a)-(f) In the plane phase diagram, the number of attractors gradually increases as the running time increases. Figure 3 (a)-(h) are control variables From the divergent graph, it can be seen that as the running time increases, the number of attractors remains unchanged, but the periodic orbits become denser. Therefore, the method of the present invention can control the divergence of attractors.

[0069] Corresponding to the method for controlling the divergence of a single variable of a memristor chaotic system over time provided in the above implementation, the present application also provides an embodiment of a device for controlling the divergence of a single variable of a memristor chaotic system over time.

[0070] See also Figure 4 In this embodiment, the device 20 for controlling the divergence of a single variable of a memristor chaotic system over time comprises:

[0071] A determination module 201 is used to determine a basic chaotic system of a single structural attractor, where the dimension of the basic chaotic system is not limited;

[0072] A construction module 202, configured to use a universal initial enhanced memristor to expand the basic chaotic system to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time;

[0073] The divergence control module 203 is used to determine the dimension according to the direction of the variable divergence and introduce a constant term, so as to control the divergence of the variable.

[0074] The present application also provides an electronic circuit, which can be implemented by analog circuit devices or digital circuit devices. The electronic circuit corresponds to a memristor chaotic system, and the divergence of a single variable over time is effectively suppressed when the electronic circuit is simulated and run.

[0075] Corresponding to the above embodiment, the embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium may store a program, wherein when the program is running, the device where the computer-readable storage medium is located may be controlled to perform some or all of the steps in the above method embodiment. In a specific implementation, the computer-readable storage medium may be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0076] Corresponding to the above-mentioned embodiment, the embodiment of the present application further provides a computer program product, which includes executable instructions. When the executable instructions are executed on a computer, the computer executes some or all of the steps in the above-mentioned method embodiment.

[0077] In the embodiments of the present application, "at least one" refers to one or more, and "plurality" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and subsequent associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0078] The above is only a specific implementation of the present application. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. The protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for controlling the divergence of a single variable of a memristor chaotic system over time, characterized in that: include: Determine a basic chaotic system of a single structural attractor, wherein the dimension of the basic chaotic system is not restricted; The basic chaotic system is extended by using a universal initial enhanced memristor to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time; The dimension is determined according to the direction in which the variable diverges and a constant term is introduced to control the divergence of the variable.

2. The method for controlling the divergence of a single variable of a memristor chaotic system over time according to claim 1, characterized in that: The basic chaotic system for determining a single structural attractor comprises: Select a basic chaotic system with a single structural attractor Said Including basic chaotic system and neuron chaotic system, expressed as: Among them, x, y, z, u are the state variables of the chaotic system, and f1, f2, f3, f4 are the state equation expressions.

3. The method for controlling the divergence of a single variable of a memristor chaotic system over time according to claim 2, characterized in that: The initial enhanced memristor It is expressed as: g, h are memristor parameters, m and e are electromagnetic induction strengths, is the internal state variable of the memristor.

4. The method for controlling the divergence of a single variable of a memristor chaotic system over time according to claim 3, characterized in that: The universal initial enhanced memristor expands the basic chaotic system to construct a memristor chaotic system, including: Exploiting the initial enhancement of memristors For basic chaotic systems Expand and construct a memristor chaotic system The following formula is used to construct the memristor chaotic system: Where x, y, z, u, is the system state variable.

5. The method for controlling the divergence of a single variable of a memristor chaotic system over time according to claim 4, characterized in that: Memristor Chaotic System By setting parameters, any number of chaotic attractors can be generated that diverge over time.

6. The method for controlling the time divergence of a single variable of a memristor chaotic system according to claim 4 or 5, characterized in that: Determine the dimension according to the direction of variable divergence and introduce a constant to control the divergence of the variable, including: According to the direction of the variable divergence, a signed constant ±m is introduced into the dimension to control the divergence of the variable. Specifically, the following formula is used: In the formula, m is a newly introduced constant.

7. A device for controlling the divergence of a single variable of a memristor chaotic system over time, characterized in that: include: A determination module, used for determining a basic chaotic system of a single structural attractor, wherein the dimension of the basic chaotic system is not restricted; A construction module, used to expand the basic chaotic system by using a universal initial enhanced memristor to construct a memristor chaotic system, wherein the memristor chaotic system can generate any number of chaotic attractors that diverge over time; The divergence control module is used to determine the dimension according to the direction of variable divergence and introduce a constant quantity to control the divergence of the variable.

8. An electronic circuit, characterized in that: Used to implement the method according to any one of claims 1 to 6.

9. A computer storage medium, characterized in that The computer-readable storage medium includes a stored program, wherein when the program is executed, the electronic device where the computer-readable storage medium is located is controlled to execute the method according to any one of claims 1 to 6.

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