Novel memristor VB5 chaotic system construction method

Abstract

The embodiment of the invention provides a novel memristor VB5 chaotic system construction method, and belongs to the technical field of data processing, and the method specifically comprises the steps: designing a target memristor; integrating the target memristor into the original VB5 chaotic system to obtain an initial VB5 chaotic system; and performing triangular transformation on the X direction in the initial VB5 chaotic system to obtain a target VB5 chaotic system. Through the scheme of the invention, starting from the internal state function of the memristor, the internal state function of the existing memristor is improved to obtain a novel and efficient memristor model, and the designed memristor is applied to the VB5 chaotic system to obtain a novel memristor VB5 chaotic system supporting multi-attractor control and growth. Through multi-attractor control and growth adaptive characteristics, the problems of insufficient flexibility in the aspects of attractor control and growth and relatively strong dependence on external parameters are effectively solved.

Description

Technical Field

[0001] Embodiments of the present disclosure relate to the technical field of data processing, and in particular, to a method for constructing a novel memristive VB5 chaotic system. Background Art

[0002] Currently, the number of multi-attractors generated by a multi-attractor chaotic system usually depends on the complex design of the memristor system. The memristor system design uses multi-segment or piecewise linear function modeling, which not only increases the complexity of model implementation but also limits its efficiency in hardware implementation. Moreover, the adjustment of parameters during the generation process lacks flexibility and it is difficult to meet the requirements for precise control of the number and characteristics of scroll attractors in practical applications. Secondly, existing memristive chaotic systems lack self-growing characteristics. Most multi-attractor chaotic systems require external input or adjustment of system parameters to achieve the expansion of the attractor structure, lacking a mechanism that can spontaneously achieve the growth of scroll attractors, which limits the system's autonomous adaptability and flexibility. And the attractor growth direction of most memristive chaotic systems is unidirectional, which limits their effectiveness in applications that require complex and controllable structure configurations.

[0003] It can be seen that there is an urgent need for a method for constructing a novel memristive VB5 chaotic system that can efficiently and precisely control the number of attractors while reducing the dependence on external intervention. Summary of the Invention

[0004] In view of this, embodiments of the present disclosure provide a method for constructing a novel memristive VB5 chaotic system, which at least partially solves the problems of insufficient flexibility in attractor control and growth and strong dependence on external parameters existing in the prior art.

[0005] Embodiments of the present disclosure provide a method for constructing a novel memristive VB5 chaotic system, including:

[0006] Step 1, designing a target memristor;

[0007] Step 2, integrating the target memristor into the original VB5 chaotic system to obtain an initial VB5 chaotic system;

[0008] Step 3, performing a triangular transformation on the X direction in the initial VB5 chaotic system to obtain a target VB5 chaotic system.

[0009] According to a specific implementation manner of the embodiments of the present disclosure, the expression of the target memristor is

[0010]

[0011] where a m , b m , c, d are internal parameters of the memristor, and i, v respectively represent the output current and input voltage of the memristor, is a non - linear memductance function, which is the internal state equation of the memristor.

[0012] According to a specific implementation manner of the embodiments of the present disclosure, the internal state equation is

[0013]

[0014] where σ = π / (4m - N + 1), sigm() is the activation function, pp is the adjustment factor of the activation function, and N is the memristor control parameter.

[0015] According to a specific implementation manner of the embodiments of the present disclosure, the expression of the initial VB5 chaotic system is

[0016]

[0017] where a, b, s, p, k are the variable parameters of the system, and x, y, z, w are the state variables.

[0018] According to a specific implementation manner of the embodiments of the present disclosure, the expression of the target VB5 chaotic system is

[0019]

[0020] The construction scheme of the novel memristive VB5 chaotic system in the embodiments of the present disclosure includes: Step 1, designing a target memristor; Step 2, integrating the target memristor into the original VB5 chaotic system to obtain an initial VB5 chaotic system; Step 3, performing a triangular transformation on the X direction in the initial VB5 chaotic system to obtain a target VB5 chaotic system.

[0021] The beneficial effects of the embodiments of the present disclosure are as follows: Through the scheme of the present disclosure, starting from the internal state function of the memristor, by improving the internal state function of the existing memristor, a novel and efficient memristor model is obtained, and the designed memristor is applied to the VB5 chaotic system to obtain a novel memristive VB5 chaotic system that supports multi - attractor control and growth. It can effectively solve the problems of insufficient flexibility in attractor control and growth and strong dependence on external parameters through the multi - attractor control and growth self - adaptive characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present disclosure. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 Flow schematic diagram of a novel memristive VB5 chaotic system construction method provided by an embodiment of the present disclosure;

[0024] Figure 2 Specific implementation process diagram of a novel memristive VB5 chaotic system construction method provided by an embodiment of the present disclosure;

[0025] Figure 3 Tight magnetic hysteresis loop curve and static break diagram of a designed memristor provided by an embodiment of the present disclosure, where (a) is the tight magnetic hysteresis loop curve and (b) is the static break diagram;

[0026] Figure 4 Bifurcation diagram and Lyapunov exponent diagram of a memristive VB5 chaotic system provided by an embodiment of the present disclosure, where (a) is the bifurcation diagram and (b) is the Lyapunov exponent diagram;

[0027] Figure 5 Phase diagrams of different numbers of multi-vortex chaotic attractors on the z-w plane under different N provided by an embodiment of the present disclosure, where (a) is the phase diagram when N is 1, (b) is the phase diagram when N is 2, (c) is the phase diagram when N is 3, and (d) is the phase diagram when N is 4;

[0028] Figure 6 Phase diagrams of a self-growing chaotic attractor at different times when N = 5 provided by an embodiment of the present disclosure, where (a) is the self-growing characteristic of the system and (b) is the bifurcation diagram;

[0029] Figure 7 Iteration results of different N values in the x-w phase diagram at different time periods provided by an embodiment of the present disclosure, where (a) are the iteration results of the x-w phase diagram when the N value is 2 at different time periods, and (b) are the iteration results of the x-w phase diagram when the N value is 3 at different time periods;

[0030] Figure 8 Structure schematic diagram of a novel memristive VB5 chaotic system implemented based on STM32 provided by an embodiment of the present disclosure. Detailed implementation

[0031] The embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0032] The following uses specific specific examples to illustrate the implementation manners of the present disclosure. Those skilled in the art can easily understand other advantages and effects of the present disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all the embodiments. The present disclosure can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present disclosure.

[0033] It should be noted that the following describes various aspects of the embodiments within the scope of the appended claims. It should be obvious that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present disclosure, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, this device and / or this method can be implemented using other structures and / or functions in addition to one or more of the aspects described herein.

[0034] It should also be noted that the drawings provided in the following embodiments only schematically illustrate the basic concept of the present disclosure. The components shown in the drawings only show the components related to the present disclosure, rather than being drawn according to the number, shape and size of the components in actual implementation. The type, quantity and proportion of each component in its actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0035] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0036] The embodiment of the present disclosure provides a method for constructing a novel memristive VB5 chaotic system, and the method can be applied to the process of constructing a chaotic system.

[0037] See Figure 1 , which is a schematic flowchart of a method for constructing a novel memristive VB5 chaotic system provided by an embodiment of the present disclosure. As Figure 1 and Figure 2 shown, the method mainly includes the following steps:

[0038] Step 1, design a target memristor;

[0039] Further, the expression of the target memristor is

[0040]

[0041] where a m , b m , c, d are internal parameters of the memristor, and i and v respectively represent the output current and input voltage of the memristor, is a non-linear memductance function, is the internal state equation of the memristor.

[0042] Further, the internal state equation is

[0043]

[0044] where σ = π / (4m - N + 1), sigm() is an activation function, pp is a regulation factor of the activation function, and N is a memristor control parameter.

[0045] In specific implementation, Figure 2 shows the construction process of the memristive VB5 chaotic system. First, a new type of memristor can be designed with the following expression:

[0046]

[0047] a m , b m , c, d are internal parameters of the memristor, and i and v respectively represent the output current and input voltage of the memristor. is a non-linear memductance function. The biggest improvement of the memristor model proposed by the present invention is the design of the function of the internal state equation, and the specific expression is as follows:

[0048]

[0049] where σ = π / (4m - N + 1), sigm() is an activation function, pp is a regulation factor of the activation function, and N is a memristor control parameter. Different from previous studies, by arbitrarily selecting different N values, any number of multi-scroll attractors can be generated. When N = 2, the tight magnetic hysteresis loop curve and its static break diagram of the designed memristor are as shown in Figure 3 shown.

[0050] Step 2: Integrate the target memristor into the original VB5 chaotic system to obtain the initial VB5 chaotic system; on the basis of the above embodiment, the expression of the initial VB5 chaotic system is

[0051]

[0052] Among them, a, b, s, p, and k are variable parameters of the system, and x, y, z, and w are state variables.

[0053] In specific implementation, after designing the target memristor, the designed memristor is then incorporated into the original VB5 chaotic system. By integrating the involved memristor, the goal is to enhance the system's ability to generate a controllable number of attractors. The resulting system is expressed as follows:

[0054]

[0055] Step 3: Perform a triangular transformation on the X direction in the initial VB5 chaotic system to obtain the target VB5 chaotic system.

[0056] Based on the above embodiments, the expression of the target VB5 chaotic system is

[0057]

[0058] In specific implementation, based on the self-replication modification method introduced in existing literature, we perform a triangular transformation on the x direction of the above system to obtain the following form, which is the target VB5 chaotic system:

[0059]

[0060] Among them, a, b, s, p, and k are variable parameters of the system, while c and d represent parameters specific to the memristor.

[0061] When b = 1, c = 2.6, d = 5.2, s = 1, p = 0.3, k = -0.15, pp = 100, and the given initial value is (0.1, 0.1, 0.1, 0.1), the bifurcation diagram and Lyapunov exponent diagram of the system are as Figure 4 shown.

[0062] The method for constructing the novel memristive VB5 chaotic system provided in this embodiment starts from the internal state function of the memristor, obtains a novel and efficient memristor model by improving the internal state function of the existing memristor, and applies the designed memristor to the VB5 chaotic system to obtain a novel memristive VB5 chaotic system that supports multi-attractor control and growth. It can effectively solve the problems of insufficient flexibility in attractor control and growth and strong dependence on external parameters through the adaptive characteristics of multi-attractor control and growth.

[0063] Traditional memristive chaotic systems have problems of insufficient flexibility in attractor control and growth, and strong dependence on external parameters, making it difficult to meet the requirements of practical applications. The memristive VB5 chaotic system proposed in this invention can effectively solve this problem through the characteristics of multi-attractor control and self-growth. This system can be widely applied in the fields of information encryption and secure communication, such as high-quality random number generation, dynamic key encryption, and chaotic modulation, etc., providing a more efficient and flexible solution for data security. In addition, this system also has significant application value in the fields of complex signal processing, biomedical signal modeling, engineering control, and energy transmission optimization, etc., and can achieve efficient and stable dynamic control under various resource-constrained conditions, fully meeting the requirements of practical engineering.

[0064] This invention proposes a memristive chaotic system that supports attractor control and self-growth by designing the combination of a new type of memristor and the VB5 chaotic system, significantly improving the dynamic regulation ability of multi-attractors and the adaptability of the system. Compared with the existing technology, this invention simplifies the modeling function of the existing memristor model, realizes the precise control of the number of attractors without complex parameter adjustment, and reduces the dependence on external intervention at the same time. This system has the characteristic of two-way self-growth, can dynamically generate multi-attractors under limited computing resources, and meets the application requirements such as efficient random number generation and dynamic key encryption. In addition, this invention optimizes the system structure design, expands its application scope in the fields of information security, signal processing, and nonlinear control, and significantly improves the practical applicability and performance of the existing chaotic system.

[0065] The method of the present disclosure will be further described below in conjunction with a specific embodiment. In order to verify how the change of N in the function in the internal state equation affects the number of attractors in the system. Through numerical simulation, we obtained the phase diagram on the w-z axis, which clearly describes the change of the number of attractors for each selected value of N, as Figure 5 shown. It can be seen from the figure that the value of N determines the number of attractors generated, thus generating N + 1 attractors. The phase diagrams of different values clearly show the vortex structures of the respective attractors, and their distribution in the phase space expands as N increases.

[0066] Attractor growth involves the dynamic expansion of the attractors of a chaotic system in the phase space as certain parameters (such as time or input gain) increase. This mechanism usually uses non-linear feedback or piecewise-based parameter control to add new layers or scroll to the attractor, gradually expanding its complexity. Figure 5 The phase diagrams of the self-growing chaotic attractors at different time points in the x-z phase plane are given with the initial values of (0.1, 0.1, 0.1, 0.1), a = 1, b = 1, c = 2.6, d = 5.2, s = 1, p = 0.3, k = -0.15, pp = 100. InFigure 6 In (a) of , it can be seen that as time goes by, the attractor structure expands, demonstrating the self-growing property of the proposed system. Figure 6 The bifurcation diagram in (b) of shows that when s > 3.2, the system enters the multi-scroll state. The selected value s = 5 satisfies this condition, illustrating the self-growing mechanism of the attractor. Existing research on self-growing chaotic attractors generally describes growth limited to a single axis and one direction. In contrast, the attractor growth mechanism proposed in this paper can achieve two-way expansion, as Figure 6 shown. The memristive chaotic system involved in the present invention has an attractor that can grow symmetrically along the positive and negative directions of the x-axis, forming a more complex and balanced multi-vortex structure.

[0067] Another advantage of the memristive chaotic system involved in the present invention is that it can effectively control the number of layers of the multi-scroll attractor through the parameter N in the designed memristor, while completing the process of self-growing replication of the attractor. Figure 7 describes the generation of multi-vortex new silver sub-structures in the system under different parameter values of N = 2 and N = 3. Among them, the magenta part represents the phase diagram generated by the system through 3000 iterations in a relatively short time period T, and the blue part represents the phase diagram formed as time goes by to T = 8000. It can be observed that as time goes by, the attractor gradually fills the specified multi-layer structure, showing a trend of dynamic growth. This growth property proves the ability of the system to expand the attractor at different numbers of layers.

[0068] This system can be widely applied to the fields of information encryption and secure communication, such as high-quality random number generation, dynamic key encryption, and chaotic modulation, etc., providing a more efficient and flexible solution for data security. In addition, this system also has significant application value in the fields of complex signal processing, biomedical signal modeling, engineering control, and energy transmission optimization, etc., and can achieve efficient and stable dynamic control under various resource-constrained conditions, fully meeting the actual engineering requirements.

[0069] Finally, as Figure 8 shown, a digital circuit based on STM32 is constructed to confirm these new findings. The proposed system can be used for both the encryption and decryption of video signals and digital watermarks, and can also be used as an independent chaotic signal generator, having wide application value in the field of nonlinear control, etc.

[0070] It should be understood that each part of the present disclosure can be implemented by hardware, software, firmware, or a combination thereof.

[0071] As described above, this is only the specific implementation manner of the present disclosure. However, the protection scope of the present disclosure is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed by the present disclosure should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure shall be subject to the protection scope of the claims.

Claims

1. A novel memristor VB5 chaotic system construction method, characterized in that: include: Step 1, design the target memristor; Step 2, integrating the target memristor into the original VB5 chaotic system to obtain the initial VB5 chaotic system; Step 3: Perform triangular transformation on the X direction of the initial VB5 chaotic system to obtain the target VB5 chaotic system.

2. The method according to claim 1, characterized in that The expression of the target memristor is: Among them, a m ,b m ,c,d are the internal parameters of the memristor, i,v represent the output current and input voltage of the memristor respectively, is a nonlinear memetic derivative function, is the internal state equation of the memristor.

3. The method according to claim 2, characterized in that The internal state equation is Wherein, σ=π / (4m-N+1), sigm() is the activation function, pp is the adjustment factor of the activation function, and N is the memristor control parameter.

4. The method according to claim 3, characterized in that The expression of the initial VB5 chaotic system is: Among them, a, b, s, p, k are variable parameters of the system, and x, y, z, w are state variables.

5. The method according to claim 4, characterized in that The expression of the target VB5 chaotic system is:

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