Estimation-resistant Lorenz chaotic derivative system establishing method

Abstract

The invention provides an anti-estimation Lorenz chaotic derivative system establishment method, and relates to the technical field of communication and information security. According to the method, the anti-estimation Lorenz chaotic derivative system is established based on the Lorenz chaotic system by utilizing a chaotic anti-control principle and introducing dynamic adjustment mechanisms such as a linear feedback control term, a high-order nonlinear coupling term and a second-order nonlinear coupling term, so that the complexity of the anti-estimation Lorenz chaotic derivative system is enhanced, the output pseudo-random sequence is more irregular, and the robustness of the system is improved. Therefore, the anti-estimation capability of an external prediction mechanism is improved, the possibility that an artificial intelligence model carries out accurate prediction through learning and fitting of system behaviors is effectively avoided, an advantageous and non-exhaustive pseudo-random sequence can be provided for a direct spread spectrum communication system, and the anti-interference capability and the concealment of the system are enhanced; meanwhile, the method can also be applied to a communication system with anti-estimation and anti-prediction requirements.

Description

Technical Field

[0001] The present invention relates to the field of communication and information security technology, and in particular to a method for establishing an estimation-resistant Lorenz chaos derivative system. Background Art

[0002] Chaotic systems are an important branch of nonlinear science, usually manifesting as complex and unpredictable dynamic behaviors under deterministic conditions. Its most notable features are its extreme sensitivity to initial conditions and the non-repeatability of long-term behavior, which makes chaotic systems a typical object for studying nonlinear dynamics and complex phenomena. The Lorenz system is one of the classic models in chaos theory. This system is based on three-dimensional ordinary differential equations and was originally used to simulate atmospheric convection, but it unexpectedly revealed the hidden chaotic characteristics of the system. A notable feature of the Lorenz system is that it exhibits complex dynamic behaviors under very simple mathematical descriptions, including extreme sensitivity to initial values, pseudo-randomness, and long-term unpredictability. Due to its simple and intuitive mathematical model, the Lorenz system has become the first choice for many applications, especially direct sequence spread spectrum communication systems, whose core is to use pseudo-random sequences to spread signals. The design of traditional pseudo-random sequences usually relies on deterministic algorithms such as linear shift registers, but chaotic systems have gradually been applied to pseudo-random sequence generation in recent years due to their pseudo-randomness and complex dynamic characteristics to improve the system's anti-interference ability and security.

[0003] However, with the rapid progress of artificial intelligence technology, especially in the field of deep learning, its powerful computing power enables artificial intelligence to effectively model and predict many types of complex dynamic systems, including the Lorenz system. Through the training of neural networks and other machine learning models, the inherent laws of the system can be extracted from a large amount of historical data, and the future behavior of the Lorenz system can be predicted. Although chaotic systems are inherently pseudo-random and long-term unpredictable, artificial intelligence makes the dynamic characteristics of the system estimable and predictable through learning and modeling, thereby making the originally unpredictable system vulnerable. This change has brought potential security risks in some high-security applications, especially in the fields of encrypted communications and information security. Therefore, it is urgent to develop a new improved Lorenz chaotic system with anti-estimation capabilities. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for establishing an estimation-resistant Lorenz chaos derivative system in view of the deficiencies of the above-mentioned prior art, which is applied to the pseudo-random sequence generation of direct sequence spread spectrum communication systems, so that it has stronger estimation-resistant capability; it can also be applied to communication systems with estimation-resistant and prediction-resistant requirements.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] The present invention provides a method for establishing an estimation-resistant Lorenz chaos derivative system, comprising the following steps:

[0007] S1. Establish the state equation of the Lorenz chaotic system, including the first, second and third system state equations. Based on the first system state equation of the Lorenz chaotic system, a linear feedback control term is introduced to obtain the first system state equation of the anti-estimation Lorenz chaotic derivative system;

[0008] The state equation of the Lorenz chaotic system is established, including the first, second and third system state equations, as shown in the following equation:

[0009]

[0010] in, is the time derivative of the state of the Lorenz chaotic system, t is the time, a, b, c are the state parameters of the Lorenz chaotic system, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, x, y, z are the independent variables of the Lorenz chaotic system;

[0011] Using the linear feedback control method in Chen chaotic system, the linear feedback control term -ex is introduced into the first system state equation of Lorenz chaotic system. Before the introduction of linear feedback anti-control, the first state equation of Lorenz chaotic system is as follows:

[0012]

[0013] Among them, f(x(t)) is the state variable of the Lorenz chaotic system, x(t) is the nonlinear dynamic term of the Lorenz chaotic system, and u(t) is the feedback signal of the external input;

[0014] Let u(t) be -ex, and after introducing the linear feedback control term, the first system state equation of the anti-estimation Lorenz chaotic derivative system is obtained as follows:

[0015]

[0016] Where, e is the feedback gain;

[0017] S2, based on the second system state equation of the Lorenz chaotic system, the linear feedback term y is discarded, and the second-order nonlinear coupling term between the two variables is introduced to obtain the second system state equation of the Lorenz chaotic derivative system that is resistant to estimation;

[0018] By discarding the linear feedback term y in the second state equation of the Lorenz chaotic system and introducing the second-order nonlinear coupling term between the two variables, the second system state equation of the anti-estimation Lorenz chaotic derivative system is obtained, as shown in the following formula:

[0019]

[0020] S3, based on the third system state equation of the Lorenz chaotic system, a high-order nonlinear coupling term is introduced to obtain the third system state equation of the Lorenz chaotic derivative system that is resistant to estimation;

[0021] Based on the third system state equation of the Lorenz chaotic system, the independent variable z is introduced to make it consistent with the third system state equation of the Lorenz chaotic system The xy terms are combined to form a high-order nonlinear coupling term of three variables, and the third system state equation of the estimation-resistant Lorenz chaotic derivative system is obtained, as shown in the following formula:

[0022]

[0023] S4, based on the first, second and third system state equations of the estimation-resistant Lorenz chaotic derivative system, establish the state equation of the estimation-resistant Lorenz chaotic derivative system, use the Runge-Kutta method to solve the state equation of the estimation-resistant Lorenz chaotic derivative system, and output the sequence solution of the x term;

[0024] Based on the first, second and third system state equations of the anti-estimation Lorenz chaos derivative system, the state equation of the anti-estimation Lorenz chaos derivative system is established, as shown in the following formula:

[0025]

[0026] in, is the time derivative of the state of the Lorenz chaotic derivative system that resists estimation, t is time, a, b, c, e are the state parameters of the Lorenz chaotic derivative system that resists estimation, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, e is the feedback gain, x′, y′, z′ are the independent variables of the Lorenz chaotic derivative system that resists estimation;

[0027] The positions of the equilibrium points of the Lorenz chaotic derivative system that is resistant to estimation are: (0,0,0),

[0028]

[0029] The Runge-Kutta method is used to solve the state equation of the Lorenz chaotic derivative system that is resistant to estimation, including the following steps:

[0030] (1) Initialize the state variables x0′, y0′ and z0′ of the estimation-resistant Lorenz chaotic derivative system;

[0031] (2) Setting the parameters of the anti-estimation Lorenz chaos derivative system, including Prandtl number a, Rayleigh number b, geometric factor c, and feedback gain e;

[0032] (3) Discretization time step;

[0033] (4) Solving the state equation of the Lorenz chaos derivative system with adversarial estimation;

[0034] (5) Output the sequence solution of the x-term of the Lorenz chaotic derivative system that is resistant to estimation;

[0035] By solving the system state equation of the estimation-resistant Lorenz chaotic derivative system, the dynamic solution of the estimation-resistant Lorenz chaotic derivative system in the time domain is obtained.

[0036] S5. Generate pseudo-random sequences for direct sequence spread spectrum communication systems based on estimation-resistant Lorenz chaos derivative systems;

[0037] The x-term sequence solution of the estimation-resistant Lorenz chaotic derivative system is extracted as the basic data of the chaotic sequence. The extracted x-term sequence solution is normalized and threshold determined. By comparing the normalized x-term sequence solution with the zero point, the normalized x-term sequence solution is converted into a binary pseudo-random sequence T. For the i-th item T in the binary pseudo-random sequence T, i , the output rule of threshold determination is as follows:

[0038]

[0039] The generated binary pseudo-random sequence T is applied to the direct sequence spread spectrum communication system to enhance the anti-interference ability and concealment of the signal.

[0040] The beneficial effect of adopting the above technical solution is that: the method for establishing a Lorenz chaos derivative system that resists estimation provided by the present invention utilizes the principle of chaos anti-control, introduces dynamic adjustment mechanisms such as linear feedback control terms, high-order nonlinear coupling terms, and second-order nonlinear coupling terms, thereby enhancing the complexity of the Lorenz chaos derivative system that resists estimation, making its output sequence more irregular, thereby improving the anti-estimation ability of the external prediction mechanism, effectively avoiding the possibility of the artificial intelligence model making accurate predictions by learning and fitting the system behavior, while retaining the original chaotic characteristics. The Lorenz chaos derivative system that resists estimation provided by the present invention greatly improves the anti-estimation ability of the system while increasing its randomness and unpredictability, especially in chaotic encryption communication and other high-security applications, providing a more stable technical guarantee. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A schematic diagram of a linear feedback control term for an estimation-resistant Lorenz chaos-derived system provided by an embodiment of the present invention;

[0042] Figure 2 Schematic diagram of the estimation-resistant Lorenz chaos derivative system provided by an embodiment of the present invention;

[0043] Figure 3 A three-dimensional phase diagram of a Lorenz chaos-derived system that is resistant to estimation provided by an embodiment of the present invention;

[0044] Figure 4 A specific flow chart of the Runge-Kutta method in the estimation-resistant Lorenz chaos-derived system provided by an embodiment of the present invention;

[0045] Figure 5 A diagram showing the prediction results of an estimation test of a generated sequence based on the BJOS method provided in an embodiment of the present invention;

[0046] Figure 6 A diagram showing the prediction results of an estimation test of a generated sequence based on the n-NODE method provided in an embodiment of the present invention;

[0047] Figure 7 A graph showing the prediction results of an estimation test of a generated sequence based on a CNN method provided in an embodiment of the present invention;

[0048] Figure 8 A graph showing the prediction results of an estimation test of a generated sequence based on the SVM method provided in an embodiment of the present invention;

[0049] Fig. 9 A graph showing the prediction results of an estimation test of a generated sequence based on the PLS method provided in an embodiment of the present invention;

[0050] Fig.10 A diagram showing the prediction results of an estimation test of a generated sequence based on the ELM method provided in an embodiment of the present invention;

[0051] Fig.11 A diagram showing the prediction results of an estimation test of a generated sequence based on the RBF method provided in an embodiment of the present invention;

[0052] Fig.12 A diagram showing the prediction results of an estimation test of a generated sequence based on the PSO-BP method provided in an embodiment of the present invention;

[0053] Fig.13 A Lyapunov exponent spectrum of an estimation-resistant Lorenz chaos-derived system provided by an embodiment of the present invention;

[0054] Fig.14 A bifurcation diagram of a Lorenz chaos-derived system that is resistant to estimation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0056] Chaotic systems are one of the core areas of nonlinear science. They usually manifest themselves as complex and unpredictable dynamic behaviors under deterministic conditions. Their most notable characteristics are their high sensitivity to initial conditions and the non-repeatability of long-term behaviors, which make them a classic object for studying nonlinear dynamics and complex phenomena.

[0057] This embodiment provides a method for establishing a Lorenz chaos derivative system that is resistant to estimation. The method of this embodiment is described as follows.

[0058] In order to study the anti-estimation performance of chaotic systems in chaotic dynamics, this embodiment is based on the ordinary differential equations of the existing traditional Lorenz chaotic system, and explores and utilizes the linear feedback control method used in the generation process of the Chen chaotic system, such as Figure 1 As shown in the figure, a linear feedback control term is introduced to enhance the balance of the dx term solution, a feedback gain is introduced to adjust the sequence amplitude of the solution, a high-order nonlinear coupling term is introduced to make the sequence distribution of the solution more complex, and a second-order nonlinear coupling term is added to increase the complexity of the phase space structure, thereby generating a Lorenz chaotic derivative system with anti-estimation performance, including the following steps:

[0059] S1. Establish the state equation of the Lorenz chaotic system, including the first, second and third system state equations. Based on the first system state equation of the Lorenz chaotic system, a linear feedback control term is introduced to obtain the first system state equation of the anti-estimation Lorenz chaotic derivative system;

[0060] The Lorenz chaotic system is a classic model in chaos theory. It was originally constructed by three-dimensional ordinary differential equations to simulate atmospheric convection, but it unexpectedly revealed its inherent chaotic characteristics. The notable feature of this system is that it can exhibit complex dynamic behaviors in a simple mathematical form, including extreme sensitivity to initial values, pseudo-randomness, and long-term unpredictability. Due to its simplicity and intuitiveness, the Lorenz system has become an ideal tool for studying chaotic phenomena and is widely used in academic research to verify the basic principles of chaos theory.

[0061] The state equation of the Lorenz chaotic system is established, including the first, second and third system state equations, as shown in the following equation:

[0062]

[0063] in, is the time derivative of the state of the Lorenz chaotic system, t is the time, a, b, c are the state parameters of the Lorenz chaotic system, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, x, y, z are the independent variables of the Lorenz chaotic system;

[0064] The linear feedback control method of chaotic system refers to making a non-chaotic system chaotic through certain control behaviors, or enhancing the chaotic behavior of an existing system. From the definition of the linear feedback control method of chaotic system, its essence is to make a non-chaotic system chaotic through control behaviors, or enhance the chaotic behavior of an existing system. Regardless of whether the system is discrete or continuous, as long as it is made chaotic or the chaotic characteristics are enhanced through control, it can be regarded as achieving chaos anti-control. Based on this idea, the linear feedback term is designed through the feedback control principle to change the system behavior and enhance its chaotic characteristics.

[0065] Using the linear feedback control method in Chen chaotic system, the linear feedback control term -ex is introduced into the first system state equation of Lorenz chaotic system. Before the introduction of linear feedback anti-control, the first state equation of Lorenz chaotic system is as follows:

[0066]

[0067] Among them, f(x(t)) is the state variable of the Lorenz chaotic system, x(t) is the nonlinear dynamic term of the Lorenz chaotic system, and u(t) is the feedback signal of the external input;

[0068] Let u(t) be -ex, and after introducing the linear feedback control term, the first system state equation of the anti-estimation Lorenz chaotic derivative system is obtained as follows:

[0069]

[0070] Where, e is the feedback gain;

[0071] In this embodiment, the feedback gain e is set to (5, 5.4); the introduced linear feedback term -ex is the system state equation An anti-control mechanism is provided to enhance the chaotic behavior of the anti-estimation Lorenz chaos derivative system and prevent the anti-estimation Lorenz chaos derivative system from experiencing short-period chaotic degradation behavior. By adjusting the feedback gain, the anti-estimation Lorenz chaos derivative system can be made to transition from a periodic orbit to a chaotic state, thereby controlling and enhancing the complexity of the anti-estimation Lorenz chaos derivative system and improving the anti-estimation characteristics of the anti-estimation Lorenz chaos derivative system.

[0072] S2, based on the second system state equation of the Lorenz chaotic system, the linear feedback term y is discarded, and the second-order nonlinear coupling term between the two variables is introduced to obtain the second system state equation of the Lorenz chaotic derivative system that is resistant to estimation;

[0073] The equilibrium point of the Lorenz chaotic system is only affected by the Rayleigh number b and the geometric factor c. The equilibrium points of the Lorenz chaotic system are: (0,0,0), This results in a relatively simple control factor for the chaotic attractor in the Lorenz chaotic system, which makes the phase space structure of the Lorenz chaotic system relatively simple and easy to analyze through phase space reconstruction, but cannot meet the requirements of anti-estimation characteristics.

[0074] By discarding the linear feedback term y in the second state equation of the Lorenz chaotic system and introducing the second-order nonlinear coupling term between the two variables, the second system state equation of the anti-estimation Lorenz chaotic derivative system is obtained, as shown in the following formula:

[0075]

[0076] By removing the original linear feedback term in the second system state equation of the Lorenz chaotic system and introducing second-order nonlinear coupling, the control parameters of the equilibrium point are changed, so that the two control parameters are changed to three control parameters to jointly control the system, the number of control parameters is increased, and the position of the chaotic attractor in the phase space is further changed, thereby improving and enhancing the nonlinear characteristics of the system, making its behavior more difficult to predict, thereby meeting the requirements of anti-estimation characteristics;

[0077] In this embodiment, by removing an original linear feedback term and introducing a second-order nonlinear coupling term between two variables, the second system state equation of the Lorenz chaotic system is improved, which solves the problem of a single chaotic attractor control factor in the Lorenz chaotic system, thereby increasing the complexity of the phase space and improving the nonlinear characteristics of the Lorenz chaotic system. This improvement effectively enhances the anti-estimation capability of the Lorenz chaotic system, making the improved anti-estimation Lorenz chaotic system more in line with the requirements of complex dynamic behavior and unpredictability in practical applications.

[0078] S3, based on the third system state equation of the Lorenz chaotic system, a high-order nonlinear coupling term is introduced to obtain the third system state equation of the Lorenz chaotic derivative system that is resistant to estimation;

[0079] In the traditional Lorenz chaotic system, the nonlinear coupling of the state equation of the third system depends only on the independent variables x and y, and lacks feedback on the independent variable z, which results in the limited nonlinear complexity of the Lorenz chaotic system, relatively simple dynamic behavior, and chaotic behavior can only be generated within a certain parameter range. By introducing high-order nonlinear coupling terms, reducing the amplitude of the solution and controlling the interval of the solution, more complex chaotic phenomena can be simulated, making the behavior of the Lorenz chaotic system more unstable and increasing the complexity of the spatial distribution of the Lorenz chaotic system.

[0080] Based on the third system state equation of the Lorenz chaotic system, the independent variable z is introduced to make it consistent with the third system state equation of the Lorenz chaotic system The xy terms are combined to form a high-order nonlinear coupling term of three variables, and the third system state equation of the estimation-resistant Lorenz chaotic derivative system is obtained, as shown in the following formula:

[0081]

[0082] After the introduction of the independent variable z, the growth behavior of z is not only affected by x and y, but also by z itself, which changes the dynamic behavior of the Lorenz chaotic system from a simple quadratic characteristic to a more complex cubic interactive behavior.

[0083] By introducing high-order nonlinear coupling terms, the behavior of the Lorenz chaotic system in space becomes richer. The nonlinear coupling orbit of the three variables is extremely sensitive to the initial value. Even if the initial difference is small, the behavior of the Lorenz chaotic system will show great differences, which increases the difficulty of estimation. The chaotic behavior in the Lorenz chaotic system usually only appears within a specific parameter range. After the introduction of high-order nonlinear coupling terms, the state space distribution of the estimation-resistant Lorenz chaotic derivative system becomes more complex, and the chaotic region is extended to a larger parameter range. Through the interaction of multiple variables, the expression range of chaotic behavior is further expanded.

[0084] S4, based on the first, second and third system state equations of the estimation-resistant Lorenz chaotic derivative system, establish the state equation of the estimation-resistant Lorenz chaotic derivative system, use the Runge-Kutta method to solve the state equation of the estimation-resistant Lorenz chaotic derivative system, and output the sequence solution of the x term;

[0085] Based on the first, second and third system state equations of the anti-estimation Lorenz chaos derivative system, the state equation of the anti-estimation Lorenz chaos derivative system is established, as shown in the following formula:

[0086]

[0087] in, is the time derivative of the state of the Lorenz chaotic derivative system that resists estimation, t is time, a, b, c, e are the state parameters of the Lorenz chaotic derivative system that resists estimation, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, e is the feedback gain, x′, y′, z′ are the independent variables of the Lorenz chaotic derivative system that resists estimation;

[0088] The positions of the equilibrium points of the Lorenz chaotic derivative system that is resistant to estimation are: (0,0,0),

[0089]

[0090] In this embodiment, the principle of the estimation-resistant Lorenz chaos derivative system is as follows: Figure 2 As shown, the three-dimensional phase diagram of the estimation-resistant Lorenz chaotic derivative system is as follows Figure 3 As shown;

[0091] The Runge-Kutta method is used to solve the system state equation of the estimation-resistant Lorenz chaotic derivative system, such as Figure 4 As shown, the following steps are included;

[0092] (1) Initialize the state variables x0′, y0′ and z0′ of the estimation-resistant Lorenz chaotic derivative system;

[0093] Initialization conditions refer to the initial state of a given system when solving ordinary differential equations. For the estimation-resistant Lorenz chaotic derivative system, three state variables x0′, y0′ and z0′ are involved. These initial conditions are determined by the background and requirements of the problem in practical applications.

[0094] (2) Setting the parameters of the anti-estimation Lorenz chaos derivative system, including Prandtl number a, Rayleigh number b, geometric factor c, and feedback gain e;

[0095] (3) Discretization time step;

[0096] Since most ordinary differential equations of chaotic systems cannot be solved analytically, it is necessary to transform the time continuous problem into a discrete problem, that is, to discretize the time. In numerical solutions, the choice of the discretization time step is crucial because it directly affects the accuracy and computational efficiency of the solution.

[0097] (4) Solving the state equation of the Lorenz chaos derivative system with adversarial estimation;

[0098] (5) Output the sequence solution of the x-term of the Lorenz chaotic derivative system that is resistant to estimation;

[0099] By solving the system state equation of the estimation-resistant Lorenz chaotic derivative system, the dynamic solution of the estimation-resistant Lorenz chaotic derivative system in the time domain is obtained.

[0100] S5. Generate pseudo-random sequences for direct sequence spread spectrum communication systems based on estimation-resistant Lorenz chaos derivative systems;

[0101] Direct sequence spread spectrum communication system is a widely used technology in modern communication, and its core is to spread the signal using a pseudo-random sequence. The design of traditional pseudo-random sequences usually relies on deterministic algorithms such as linear shift registers, but chaotic systems have gradually been applied to pseudo-random sequence generation in recent years due to their pseudo-randomness and complex dynamic characteristics, which are used to improve the anti-interference ability and security of the system. In order to cope with the security threats brought by artificial intelligence modeling, this embodiment uses the sequence generated by the anti-estimation Lorenz chaos derivative system for the pseudo-random sequence generation of the direct sequence spread spectrum communication system, so that the pseudo-random sequence of the direct sequence spread spectrum communication system has a stronger anti-estimation ability; at the same time, the anti-estimation Lorenz chaos derivative system can also be applied to communication systems with anti-estimation and anti-prediction requirements.

[0102] The x-term sequence solution of the estimation-resistant Lorenz chaotic derivative system is extracted as the basic data of the chaotic sequence. The extracted x-term sequence solution is normalized and threshold determined. By comparing the normalized x-term sequence solution with the zero point, the normalized x-term sequence solution is converted into a binary pseudo-random sequence T. For the i-th item T in the binary pseudo-random sequence T, i , the output rule of threshold determination is as follows:

[0103]

[0104] The generated binary pseudo-random sequence T is applied to the direct sequence spread spectrum communication system as a spread spectrum code to spread the signal, thereby enhancing the anti-interference ability and concealment of the signal.

[0105] In this embodiment, in order to verify the anti-estimation ability of the sequence generated by the anti-estimation Lorenz chaos derivative system, 8 methods are used to estimate the generated pseudo-random sequence, including: a short-term prediction method based on joint order phase space reconstruction and Bayesian optimized back propagation network (BJOS), n-dimensional chaotic time series optimization blind estimation (n-NODE), convolutional neural network (CNN), support vector machine (SVM), partial least squares regression (PLS), extreme learning machine (ELM), radial basis function network (RBF), and particle swarm optimized back propagation neural network (PSO-BP), among which, the BJOS and n-NODE estimation methods use a training test data set of 500 steps and predict the next 200 steps. The prediction results are as follows: Figure 5 and Figure 6 As shown; CNN, SVM, PLS, ELM, RBF, PSO-BP estimation methods use a training test data set of 700 steps to predict the next 1 step. The prediction results are as follows Figure 7-Figure 12 As shown, due to the phase space reconstruction, the prediction of the next 220 steps actually represents 1 step in the future.

[0106] Depend on Figure 5-Figure 12 It can be seen that after using BJOS, n-NODE, CNN, SVM, PLS, ELM, RBF, and PSO-BP methods to estimate the pseudo-random sequence generated by the estimation-resistant Lorenz chaos derivative system, these algorithms failed to effectively predict the regularity or future state of the sequence. This shows that the pseudo-random sequence generated by the estimation-resistant Lorenz chaos derivative system is highly nonlinear and complex, and its pseudo-random characteristics make it difficult for these models to extract usable estimation patterns from the data. This further shows that the pseudo-random sequence generated by the estimation-resistant Lorenz chaos derivative system has a high anti-estimation performance.

[0107] In this embodiment, in order to comprehensively evaluate the chaotic characteristics of the estimation-resistant Lorenz chaotic derivative system, the Lyapunov exponent spectrum and bifurcation diagram are tested and analyzed. The Lyapunov exponent spectrum of the estimation-resistant Lorenz chaotic derivative system is shown in FIG. Fig.13 As shown in the figure, when parameters a and b are fixed, the change of Lyapunov index spectrum with the change of parameter c is tested. It can be seen from the figure that its three indexes are all greater than 0, indicating that the estimation-resistant Lorenz chaotic derivative system has chaotic characteristics; when parameters a and c are fixed, the bifurcation diagram of the system independent variable z′ with the change of parameter b is as follows Fig.14 As shown, Fig.14 The dynamic behavior of the system independent variable z′ is demonstrated when the parameter b is greater than 10, further proving the chaotic characteristics of the estimation-resistant Lorenz chaotic derivative system.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for establishing an estimation-resistant Lorenz chaotic derivative system, characterized in that: The following steps are involved: S1. Establish the state equation of the Lorenz chaotic system, including the first, second and third system state equations. Based on the first system state equation of the Lorenz chaotic system, a linear feedback control term is introduced to obtain the first system state equation of the anti-estimation Lorenz chaotic derivative system; S2, based on the second system state equation of the Lorenz chaotic system, the linear feedback term y is discarded, and the second-order nonlinear coupling term between the two variables is introduced to obtain the second system state equation of the Lorenz chaotic derivative system that is resistant to estimation; S3, based on the third system state equation of the Lorenz chaotic system, a high-order nonlinear coupling term is introduced to obtain the third system state equation of the Lorenz chaotic derivative system that is resistant to estimation; S4, based on the first, second and third system state equations of the estimation-resistant Lorenz chaotic derivative system, establish the state equation of the estimation-resistant Lorenz chaotic derivative system, use the Runge-Kutta method to solve the state equation of the estimation-resistant Lorenz chaotic derivative system, and output the sequence solution of the x term; S5. Generate pseudo-random sequences for direct sequence spread spectrum communication systems based on an estimation-resistant Lorenz chaotic derivative system.

2. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 1, characterized in that: The specific method of S1 is: The state equation of the Lorenz chaotic system is established, including the first, second and third system state equations, as shown in the following equation: in, is the time derivative of the state of the Lorenz chaotic system, t is the time, a, b, c are the state parameters of the Lorenz chaotic system, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, x, y, z are the independent variables of the Lorenz chaotic system; Using the linear feedback control method in Chen chaotic system, the linear feedback control term -ex is introduced into the first system state equation of Lorenz chaotic system. Before the introduction of linear feedback anti-control, the first state equation of Lorenz chaotic system is as follows: Among them, f(x(t)) is the state variable of the Lorenz chaotic system, x(t) is the nonlinear dynamic term of the Lorenz chaotic system, and u(t) is the feedback signal of the external input; Let u(t) be -ex, and after introducing the linear feedback control term, the first system state equation of the anti-estimation Lorenz chaotic derivative system is obtained as follows: Where e is the feedback gain.

3. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 2, characterized in that: The specific method of S2 is: By discarding the linear feedback term y in the second state equation of the Lorenz chaotic system and introducing the second-order nonlinear coupling term between the two variables, the second system state equation of the anti-estimation Lorenz chaotic derivative system is obtained, as shown in the following formula:

4. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 3, characterized in that: The S3 specific method is: Based on the third system state equation of the Lorenz chaotic system, the independent variable z is introduced to make it consistent with the third system state equation of the Lorenz chaotic system The xy terms are combined to form a high-order nonlinear coupling term of three variables, and the third system state equation of the estimation-resistant Lorenz chaotic derivative system is obtained, as shown in the following formula:

5. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 4, characterized in that: The specific method of S4 to establish the state equation of the Lorenz chaos derivative system that is resistant to estimation is: Based on the first, second and third system state equations of the anti-estimation Lorenz chaos derivative system, the state equation of the anti-estimation Lorenz chaos derivative system is established, as shown in the following formula: in, is the time derivative of the state of the Lorenz chaotic derivative system that resists estimation, t is the time, a, b, c, e are the state parameters of the Lorenz chaotic derivative system that resists estimation, a is the Prandtl number, b is the Rayleigh number, c is the geometric factor, e is the feedback gain, x′, y′, z′ are the independent variables of the Lorenz chaotic derivative system that resists estimation.

6. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 5, characterized in that: The positions of the equilibrium points of the Lorenz chaotic derivative system that is resistant to estimation are: (0,0,0), 7. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 6, characterized in that: The S4 uses the Runge-Kutta method to solve the state equation of the Lorenz chaos-derived system that is resistant to estimation, including the following steps: (1) Initialize the state variables x′0, y′0 and z′0 of the Lorenz chaotic derivative system that is resistant to estimation; (2) Setting the parameters of the anti-estimation Lorenz chaos derivative system, including Prandtl number a, Rayleigh number b, geometric factor c, and feedback gain e; (3) Discretization time step; (4) Solving the state equation of the Lorenz chaos derivative system with adversarial estimation; (5) Output the sequence solution of the x-term of the Lorenz chaotic derivative system that is resistant to estimation; By solving the system state equation of the estimation-resistant Lorenz chaotic derivative system, the dynamic solution of the estimation-resistant Lorenz chaotic derivative system in the time domain is obtained.

8. The method for establishing a Lorenz chaos derivative system resistant to estimation according to claim 7, characterized in that: The specific method of S5 is: The x-term sequence solution of the estimation-resistant Lorenz chaotic derivative system is extracted as the basic data of the chaotic sequence. The extracted x-term sequence solution is normalized and threshold determined. By comparing the normalized x-term sequence solution with the zero point, the normalized x-term sequence solution is converted into a binary pseudo-random sequence T. For the i-th item T in the binary pseudo-random sequence T, i , the output rule of threshold determination is as follows: The generated binary pseudo-random sequence T is applied to the direct sequence spread spectrum communication system to enhance the anti-interference ability and concealment of the signal.

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