Method and device for selecting optimal value of hyper-chaos four-dimensional system parameter

Abstract

The invention relates to a method and a device for selecting an optimal value of a hyper-chaos four-dimensional system parameter, and belongs to the technical field of hyper-chaos systems.The method comprises the following steps: selecting a hyper-chaos four-dimensional system with a large LE value, performing performance analysis, and determining a solving sequence of the solved parameter and the optimal value of the parameter; solving the time sequence of the hyperchaotic four-dimensional system variable, and performing stability analysis; performing hyper-chaos characteristic analysis on the hyper-chaos four-dimensional system of which the solved parameters are in the initial value range, and obtaining a hyper-chaos characteristic value range of the solved parameters when the hyper-chaos four-dimensional system is always in a hyper-chaos state; judging the stability of the hyper-chaos four-dimensional system variable in the hyper-chaos characteristic value range of the solved parameter, determining the final value range of the solved parameter when the hyper-chaos four-dimensional system variable is stable, and calculating the optimal value and the maximum LE value of the solved parameter. According to the method, the LE value of the hyper-chaos four-dimensional system is improved, and then the randomness of the hyper-chaos four-dimensional system is improved.

Description

Technical Field

[0001] The invention relates to a method and a device for selecting optimal values ​​of hyperchaotic four-dimensional system parameters, belonging to the technical field of hyperchaotic systems. Background Art

[0002] A chaotic system is a complex nonlinear system with the characteristics of boundedness, topological ergodicity, randomness or sensitivity to initial values. The signals it generates are random, non-repetitive and unpredictable. It is widely used in communication signal encryption, image compression encryption, and the construction of chaotic robots that perform special tasks such as full coverage path planning, and other occasions that require high randomness and information confidentiality.

[0003] According to the dimension of the system, chaotic systems are mainly divided into low-dimensional chaotic systems and high-dimensional hyperchaotic systems. Low-dimensional chaotic systems have simple structures and low system complexity, which can meet the occasions with low randomness requirements; however, they have problems such as simple phase space and few parameters, which makes the signal encryption effect poor and easy to be cracked. Compared with low-dimensional chaos, high-dimensional hyperchaotic systems have complex mapping and many control parameters, so they are more chaotic and random, and are generally composed of four-dimensional and above chaotic systems. Hyperchaotic systems have at least two positive Lyapunov exponents (LE). The larger the positive LE index, the stronger its randomness. Many scholars have proposed many hyperchaotic systems with excellent performance and their construction methods to improve the chaos and randomness of hyperchaotic systems and meet the needs of high-randomness signals such as image encryption and chaotic robot construction.

[0004] At present, the literature uses hyperchaotic four-dimensional systems to generate high-random signals for application. One is to directly use an existing hyperchaotic system with good random performance, or to construct one based on a low-dimensional chaotic system. The control of hyperchaotic system parameters is complex, and there is currently a lack of systematic research on the influence of hyperchaotic system parameter combinations on the random performance of the system. Some literature only discusses the values ​​of several sets of typical parameter data in a simple and qualitative manner through phase planes, phase spaces and other graphical methods. There is a lack of quantitative calculation of the influence of hyperchaotic system parameter values ​​on the random performance of the system, and there is no discussion on the stability of variables when the system is in a hyperchaotic state. The stable change of variables affects the trajectory distribution of the signal. Hyperchaotic systems have many parameters and a wide range of parameter values ​​when they are in a hyperchaotic state. Which parameter combination can make the hyperchaotic system obtain higher randomness and stability? How to obtain the optimal parameter value faster is an urgent problem to be solved in the application of hyperchaotic systems. Summary of the invention

[0005] The present invention proposes a method and device for selecting optimal values ​​of hyperchaotic four-dimensional system parameters, which can select parameter values ​​with stable system variable changes and good trajectory traversal performance, improve the LE value of the system, and thus improve the randomness of the system.

[0006] The technical solution adopted by the present invention to solve the technical problem is:

[0007] In a first aspect, an embodiment of the present invention provides a method for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system, comprising the following steps:

[0008] Step S1, selecting a hyperchaotic four-dimensional system with a large LE value and performing performance analysis to determine the parameters to be sought and their initial values ​​and the order in which the optimal values ​​of the parameters are sought;

[0009] Step S2, solving the time series of the hyperchaotic four-dimensional system variables and performing stability analysis on the hyperchaotic four-dimensional system variables;

[0010] Step S3, performing a hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system whose desired parameter is within the initial value range, and obtaining a hyperchaotic characteristic value range of the desired parameter when the hyperchaotic four-dimensional system is always in a hyperchaotic state;

[0011] Step S4, judging the stability of the hyperchaotic four-dimensional system variable within the hyperchaotic characteristic value range of the desired parameter, if it is stable, proceeding to step S3, and continuing to adjust the value range of the desired parameter of the hyperchaotic system according to the greedy strategy; otherwise, narrowing the value range of the parameter, determining the final value range of the desired parameter when the hyperchaotic four-dimensional system variable is stable, and proceeding to step S5;

[0012] Step S5, calculating the optimal value of the required parameter and the maximum LE value.

[0013] As a possible implementation of this embodiment, step S1 includes the following steps:

[0014] Step S11, selecting a hyperchaotic four-dimensional system with a large LE value from the hyperchaotic four-dimensional systems constructed in the existing literature;

[0015] Step S12, determining the order of solving the required parameters, the initial parameter values ​​of the required parameters and the optimal parameter values ​​according to the selected hyperchaotic four-dimensional system structure;

[0016] Step S13, analyzing the LE value and dissipativeness of the selected hyperchaotic four-dimensional system to ensure that it has two positive and large LE values.

[0017] As a possible implementation of this embodiment, step S2 includes the following steps:

[0018] Step S21, the selected hyperchaotic four-dimensional system with a large LE value is used to calculate the time series (x, y, z, w) of the four variables (x, y, z, w) in the hyperchaotic four-dimensional system according to the given parameter values ​​and the fourth-order Runge-Kutta formula. n,y n ,z n ,w n ):

[0019] Use the fourth-order Runge-Kutta formula to calculate the time series x of one variable x n , the formula is as follows:

[0020]

[0021] Among them, x is a variable in the hyperchaotic four-dimensional system, x n is the time series of variable x, f(·) is the structure of the selected hyperchaotic four-dimensional system, Δt is the sampling time, h is the iteration step, and the subscript n represents the number of iterations;

[0022] Step S22, according to the obtained time series (x n ,y n ,z n ,w n ) Analyze the performance of variables under stable and abnormal conditions to determine the causes of abnormal conditions.

[0023] As a possible implementation of this embodiment, step S3 includes the following steps:

[0024] Step S31, determining an initial value range of the desired parameter with the initial value of the desired parameter as the center, calculating two positive LE indexes within the initial value range by using the time series of the hyperchaotic four-dimensional system variables, and drawing the LE index spectrum;

[0025] Step S32, according to the obtained parameter L at each value E1 and L E2 The value is judged, the parameter value corresponding to the negative LE value is eliminated, and then the value range of the parameter p is readjusted in the direction of increasing the LE value according to the greedy strategy. min and p max ; Ensure that the two LE values ​​are always positive within the parameter value range, that is, the system is always in a hyperchaotic state.

[0026] As a possible implementation of this embodiment, step S31 includes the following steps:

[0027] Assume that the current parameter is p, the initial parameter value is p0, and determine a value range p∈[p min ,p max ], satisfying p min <p0<p max , calculate p∈[p according to the LE value calculation formula min ,p max], the two largest LE indices with integer values ​​of parameter p are denoted as L E1 and L E2 , and draw the corresponding LE index spectrum to observe L E1 and L E2 The values ​​in this range must satisfy that both sequence values ​​are positive numbers. The LE value calculation formula is:

[0028]

[0029] Among them, △D0 is the length of the two initial values, △D i is the distance between the i-th variables, i=1~n;

[0030] In p∈[p min ,p max Each LE value of the system within the range of ] needs to be calculated N size Index, N size =p max -p min , is L E1 and L E2 Length;

[0031] In the hyperchaotic four-dimensional system, take two very close initial values ​​X0 and X0' of the variables, X0 = (x0, y0, z0, w0), X0' = (x0', y0', z0', w0'), and calculate two sample sequences X of length n according to the two initial values ​​and formula (1). n and X n ', X n =(x n ,y n ,z n ,w n ), X n '=(x n ',y n ',z n ',w n ');

[0032] In the parameter p∈[p min ,p max ], a total of N size LE index.

[0033] As a possible implementation of this embodiment, step S4 includes the following steps:

[0034] Step S41: Take the variable time series X under N normal states and M abnormal states according to the required parameter p i =(x i ,y i ,z i,w i ),i=1,...,N;X j =(x j ,y j ,z j ,w j ),j=1,...,M;

[0035] Step S42, find the mean of the variable time series under each value of parameter p and

[0036]

[0037] Step S43, respectively calculate the sample standard deviation σ of parameter p under N normal states and M abnormal states k and σ k ':

[0038]

[0039] Where n is the length of each variable time series;

[0040] Step S44: taking the average value of the sample standard deviation of parameter p under N normal conditions as the comparison value

[0041]

[0042] Step S45, using formula (4) to calculate the σ value of parameter p under the test value;

[0043] Step S46, calculate the sample standard deviation ratio K σ :

[0044]

[0045] Step S47: according to the sample standard deviation ratio K of the variable under normal state and abnormal state, σ The difference between the two sets of samples sets the threshold K of the sample standard deviation ratio. th , if K σ <K th , it means that the chaotic system variables change stably, that is, it is running on the normal track; otherwise, it is an abnormal state;

[0046] Step S48: If the chaotic system variables change stably, go to step S3 and continue to adjust the value range of the parameters required by the hyperchaotic system according to the greedy strategy; if the chaotic system variables change to an abnormal state, narrow the value range of the parameters, determine the final value range of the parameters required when the hyperchaotic four-dimensional system variables are stable, and go to step S5.

[0047] As a possible implementation of this embodiment, step S5 includes the following steps:

[0048] Step S51: according to the final value range of the parameter to be sought, E1 Find the maximum LEmax and its location LEmax_id:

[0049] [LEmax, LEmax_id] = max(L E1 ) (7);

[0050] Step S52, obtain the maximum L E1 The value of parameter p LE :

[0051]

[0052] Then the final p LE The value is the optimal value of parameter p that can enable the system to obtain the best randomness.

[0053] In a second aspect, an embodiment of the present invention provides a device for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system, comprising:

[0054] The system selection and analysis module is used to select a hyperchaotic four-dimensional system with a large LE value and perform performance analysis to determine the parameters and their initial values ​​and the order of solving the optimal parameter values;

[0055] The time series solving module is used to solve the time series of the hyperchaotic four-dimensional system variables and to perform stability analysis on the hyperchaotic four-dimensional system variables;

[0056] A hyperchaotic characteristic analysis module is used to analyze the hyperchaotic characteristics of a hyperchaotic four-dimensional system whose parameters are within an initial value range, and obtain a hyperchaotic characteristic value range of the parameters when the hyperchaotic four-dimensional system is always in a hyperchaotic state;

[0057] The stability judgment module is used to judge the stability of the hyperchaotic four-dimensional system variables within the hyperchaotic characteristic value range of the required parameters. If the hyperchaotic four-dimensional system variables are stable, the hyperchaotic characteristic analysis module is used to perform hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system with the required parameters within the initial value range, and the value range of the required parameters of the hyperchaotic system is adjusted according to the greedy strategy; otherwise, the value range of the parameters is reduced to determine the final value range of the required parameters when the hyperchaotic four-dimensional system variables are stable.

[0058] The optimal value calculation module is used to calculate the optimal value of the required parameter and the maximum LE value.

[0059] In the third aspect, an embodiment of the present invention provides an electronic device, including a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory through the bus, and the processor executes the machine-readable instructions to perform the steps of the method for selecting the optimal values ​​of any hyperchaotic four-dimensional system parameters as described above.

[0060] In a fourth aspect, an embodiment of the present invention provides a storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method for selecting the optimal values ​​of any hyperchaotic four-dimensional system parameter as described above are executed.

[0061] The beneficial effects of the technical solution of the embodiment of the present invention are as follows:

[0062] A method for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system according to the technical solution of an embodiment of the present invention comprises the following steps: step S1, selecting a hyperchaotic four-dimensional system with a large LE value and performing performance analysis to determine the order of solving the required parameters and their initial values ​​and the optimal values ​​of the parameters; step S2, solving the time series of the variables of the hyperchaotic four-dimensional system and performing stability analysis on the variables of the hyperchaotic four-dimensional system; step S3, performing hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system whose parameters are within the initial value range to obtain Take the hyperchaotic characteristic value range of the parameter to be sought when the hyperchaotic four-dimensional system is always in a hyperchaotic state; step S4, judge the stability of the hyperchaotic four-dimensional system variable within the hyperchaotic characteristic value range of the parameter to be sought, if it is stable, go to step S3, and continue to adjust the value range of the parameter to be sought in the hyperchaotic system according to the greedy strategy; otherwise, narrow the value range of the parameter, determine the final value range of the parameter to be sought when the hyperchaotic four-dimensional system variable is stable, and go to step S5; step S5, calculate the optimal value and maximum LE value of the parameter to be sought. The present invention provides a research idea for further improving chaos and randomness of a hyperchaotic system with a high LE value, improves the LE value of the system by selecting the optimal parameter value of the system, thereby improving the randomness of the system; provides a parameter search direction through a greedy strategy, searches along the direction of increasing LE value to improve the search speed of the optimal parameter value; specifically calculates the change of the system variable through the sample standard deviation, thereby selecting the parameter value with stable change of the system variable and good trajectory traversal performance.

[0063] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0064] 1. The present invention realizes the selection of optimal parameter values ​​of a hyperchaotic four-dimensional system using a greedy strategy, provides a search direction for parameter values, and searches in the direction of increasing the system LE value to improve the search speed for the optimal parameter values.

[0065] 2. The present invention realizes the use of sample standard deviation method to calculate and analyze the change characteristics of hyperchaotic four-dimensional system variables, and judges whether the change of system variables is stable, that is, whether it deviates from the normal operating track through qualitative calculation.

[0066] 3. The present invention realizes the discussion and calculation of the stability of variable changes when the hyperchaotic four-dimensional system is in a hyperchaotic state, and can select a trajectory with stable system variable changes and good distribution performance from different parameter values.

[0067] 4. The present invention can further improve the chaos and randomness of a hyperchaotic four-dimensional system with a large LE value in a simple and easy way.

[0068] 5. The present invention is universal and applicable not only to hyperchaotic four-dimensional systems, but also to hyperchaotic systems with dimensions above four. It is not only applicable to hyperchaotic systems with large LE values, but also to small LE hyperchaotic systems with low random performance. The LE value can be increased in this way, thereby improving the randomness of the hyperchaotic four-dimensional system. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of a method for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system according to an exemplary embodiment;

[0070] Figure 2 It is a structural schematic diagram of a device for selecting optimal values ​​of hyperchaotic four-dimensional system parameters according to an exemplary embodiment;

[0071] Figure 3 This is a specific implementation process flow chart of the present invention for selecting the optimal value of the hyperchaotic four-dimensional system parameter;

[0072] Figure 4 is a schematic diagram of a time series (normal state) of four variables when seven parameters take initial values ​​according to an exemplary embodiment;

[0073] Figure 5 is a schematic diagram of a phase plane (normal state) of two variables when seven parameters take initial values ​​according to an exemplary embodiment;

[0074] Figure 6 It is a schematic diagram of a time series (abnormal state) when a parameter a=217 and other six parameters take initial values ​​according to an exemplary embodiment;

[0075] Figure 7 It is a schematic diagram of phase plane (abnormal state) of two variables when parameter a=217 and other six parameters take initial values ​​according to an exemplary embodiment;

[0076] Figure 8is a schematic diagram of an exponential spectrum of a system when a parameter a∈[40,120] is shown according to an exemplary embodiment;

[0077] Fig. 9 is a schematic diagram of an exponential spectrum of a system when a parameter a∈[70,120] is shown according to an exemplary embodiment;

[0078] Fig.10 is a sample standard deviation K of four variables of a parameter a under 40 normal conditions according to an exemplary embodiment. σ ratio graph;

[0079] Fig.11 is a sample standard deviation K of four variables of a parameter a under 10 abnormal conditions according to an exemplary embodiment. σ ratio graph;

[0080] Fig.12 is a K of four variables of a parameter a under 40 normal states and 10 abnormal states according to an exemplary embodiment. σ Schematic diagram of value comparison;

[0081] Fig.13 is a parameter a∈[70,120] according to an exemplary embodiment. σ Value diagram;

[0082] Fig.14 is a schematic diagram of an exponential spectrum of a system when a parameter a∈[120,220] is shown according to an exemplary embodiment;

[0083] Fig.15 is a parameter a∈[120,220] according to an exemplary embodiment. σ Value diagram;

[0084] Fig.16 It is a schematic diagram of an exponential spectrum of a system when a parameter r∈[90,110] is shown according to an exemplary embodiment (the other six parameters take optimal values). DETAILED DESCRIPTION

[0085] In order to more clearly illustrate the technical features of the solution of the present invention, the present invention is described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0086] like Figure 1 As shown, a method for selecting optimal values ​​of hyperchaotic four-dimensional system parameters provided by an embodiment of the present invention includes the following steps:

[0087] Step S1, selecting a hyperchaotic four-dimensional system with a large LE value and performing performance analysis to determine the parameters to be sought and their initial values ​​and the order in which the optimal values ​​of the parameters are sought;

[0088] Step S2, solving the time series of the hyperchaotic four-dimensional system variables and performing stability analysis on the hyperchaotic four-dimensional system variables;

[0089] Step S3, performing a hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system whose desired parameter is within the initial value range, and obtaining a hyperchaotic characteristic value range of the desired parameter when the hyperchaotic four-dimensional system is always in a hyperchaotic state;

[0090] Step S4, judging the stability of the hyperchaotic four-dimensional system variable within the hyperchaotic characteristic value range of the desired parameter, if it is stable, proceeding to step S3, and continuing to adjust the value range of the desired parameter of the hyperchaotic system according to the greedy strategy; otherwise, narrowing the value range of the parameter, determining the final value range of the desired parameter when the hyperchaotic four-dimensional system variable is stable, and proceeding to step S5;

[0091] Step S5, calculating the optimal value of the required parameter and the maximum LE value.

[0092] As a possible implementation of this embodiment, step S1 includes the following steps:

[0093] Step S11, selecting a hyperchaotic four-dimensional system with a large LE value from the hyperchaotic four-dimensional systems constructed in the existing literature;

[0094] Step S12, determining the order of solving the required parameters, the initial parameter values ​​of the required parameters and the optimal parameter values ​​according to the selected hyperchaotic four-dimensional system structure;

[0095] Step S13, analyzing the LE value and dissipativeness of the selected hyperchaotic four-dimensional system to ensure that it has two positive and large LE values.

[0096] As a possible implementation of this embodiment, step S2 includes the following steps:

[0097] Step S21, the selected hyperchaotic four-dimensional system with a large LE value is used to calculate the time series (x, y, z, w) of the four variables (x, y, z, w) in the hyperchaotic four-dimensional system according to the given parameter values ​​and the fourth-order Runge-Kutta formula. n ,y n ,z n ,w n ):

[0098] Use the fourth-order Runge-Kutta formula to calculate the time series x of one variable x n , the formula is as follows:

[0099]

[0100] Among them, x is a variable in the hyperchaotic four-dimensional system, x n is the time series of variable x, f(·) is the structure of the selected hyperchaotic four-dimensional system, Δt is the sampling time, h is the iteration step, and the subscript n represents the number of iterations;

[0101] Step S22, according to the obtained time series (x n ,y n ,z n ,w n ) Analyze the performance of variables under stable and abnormal conditions to determine the causes of abnormal conditions.

[0102] As a possible implementation of this embodiment, step S3 includes the following steps:

[0103] Step S31, determining an initial value range of the desired parameter with the initial value of the desired parameter as the center, calculating two positive LE indexes within the initial value range by using the time series of the hyperchaotic four-dimensional system variables, and drawing the LE index spectrum;

[0104] Step S32, according to the obtained parameter L at each value E1 and L E2 The value is judged, the parameter value corresponding to the negative LE value is eliminated, and then the value range of the parameter p is readjusted in the direction of increasing the LE value according to the greedy strategy. min and p max ; Ensure that the two LE values ​​are always positive within the parameter value range, that is, the system is always in a hyperchaotic state.

[0105] As a possible implementation of this embodiment, step S31 includes the following steps:

[0106] Assume that the current parameter is p, the initial parameter value is p0, and determine a value range p∈[p min ,p max ], satisfying p min <p0<p max , calculate p∈[p according to the LE value calculation formula min ,p max ], the two largest LE indices with integer values ​​of parameter p are denoted as L E1 and L E2 , and draw the corresponding LE index spectrum to observe L E1 and L E2 The values ​​in this range must satisfy that both sequence values ​​are positive numbers. The LE value calculation formula is:

[0107]

[0108] Among them, △D0 is the length of the two initial values, △D i is the distance between the i-th variables, i=1~n;

[0109] In p∈[p min ,p max Each LE value of the system within the range of ] needs to be calculated N size Index, N size =p max -p min , is L E1 and L E2 Length;

[0110] In the hyperchaotic four-dimensional system, take two very close initial values ​​X0 and X0' of the variables, X0 = (x0, y0, z0, w0), X0' = (x0', y0', z0', w0'), and calculate two sample sequences X of length n according to the two initial values ​​and formula (1). n and X n ', X n =(x n ,y n ,z n ,w n ), X n '=(x n ',y n ',z n ',w n ');

[0111] In the parameter p∈[p min ,p max ], a total of N size LE index.

[0112] As a possible implementation of this embodiment, step S4 includes the following steps:

[0113] Step S41: Take the variable time series X under N normal states and M abnormal states according to the required parameter p i =(x i ,y i ,z i ,w i ),i=1,...,N;X j =(x j ,y j ,z j ,w j ),j=1,...,M;

[0114] Step S42, find the mean of the variable time series under each value of parameter p and

[0115]

[0116] Step S43, respectively calculate the sample standard deviation σ of parameter p under N normal states and M abnormal states k and σ k ':

[0117]

[0118] Where n is the length of each variable time series;

[0119] Step S44: taking the average value of the sample standard deviation of parameter p under N normal conditions as the comparison value

[0120]

[0121] Step S45, using formula (4) to calculate the σ value of parameter p under the test value;

[0122] Step S46, calculate the sample standard deviation ratio K σ :

[0123]

[0124] Step S47: according to the sample standard deviation ratio K of the variable under normal state and abnormal state, σ The difference between the two sets of samples sets the threshold K of the sample standard deviation ratio. th , if K σ <K th , it means that the chaotic system variables change stably, that is, it is running on the normal track; otherwise, it is an abnormal state;

[0125] Step S48: If the chaotic system variables change stably, go to step S3 and continue to adjust the value range of the parameters required by the hyperchaotic system according to the greedy strategy; if the chaotic system variables change to an abnormal state, narrow the value range of the parameters, determine the final value range of the parameters required when the hyperchaotic four-dimensional system variables are stable, and go to step S5.

[0126] As a possible implementation of this embodiment, step S5 includes the following steps:

[0127] Step S51: according to the final value range of the parameter to be sought, E1 Find the maximum LEmax and its location LEmax_id:

[0128] [LEmax, LEmax_id] = max(L E1 ) (7);

[0129] Step S52, obtain the maximum L E1 The value of parameter p LE :

[0130]

[0131] Then the final p LE The value is the optimal value of parameter p that can enable the system to obtain the best randomness.

[0132] like Figure 2 As shown, an embodiment of the present invention provides a device for selecting optimal values ​​of hyperchaotic four-dimensional system parameters, comprising:

[0133] The system selection and analysis module is used to select a hyperchaotic four-dimensional system with a large LE value and perform performance analysis to determine the parameters and their initial values ​​and the order of solving the optimal parameter values;

[0134] The time series solving module is used to solve the time series of the hyperchaotic four-dimensional system variables and to perform stability analysis on the hyperchaotic four-dimensional system variables;

[0135] A hyperchaotic characteristic analysis module is used to analyze the hyperchaotic characteristics of a hyperchaotic four-dimensional system whose parameters are within an initial value range, and obtain a hyperchaotic characteristic value range of the parameters when the hyperchaotic four-dimensional system is always in a hyperchaotic state;

[0136] The stability judgment module is used to judge the stability of the hyperchaotic four-dimensional system variables within the hyperchaotic characteristic value range of the required parameters. If the hyperchaotic four-dimensional system variables are stable, the hyperchaotic characteristic analysis module is used to perform hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system with the required parameters within the initial value range, and the value range of the required parameters of the hyperchaotic system is adjusted according to the greedy strategy; otherwise, the value range of the parameters is reduced to determine the final value range of the required parameters when the hyperchaotic four-dimensional system variables are stable.

[0137] The optimal value calculation module is used to calculate the optimal value of the required parameter and the maximum LE value.

[0138] like Figure 3 As shown, a specific implementation process of the present invention for selecting the optimal values ​​of hyperchaotic four-dimensional system parameters is as follows.

[0139] 1) Select and analyze the performance of a hyperchaotic four-dimensional system with a large LE value, and determine the system parameters to be solved and the order in which the optimal parameter values ​​are solved.

[0140] 1.1) Selection of hyperchaotic four-dimensional systems with large LE values.

[0141] Among the hyperchaotic four-dimensional systems constructed in the existing literature, a system with a large LE value is selected. The larger the two positive LE values, the better. Here, a new hyperchaotic four-dimensional system designed by Lijuan Chen et al. is selected. For more information, see the literature [1]: Lijuan Chen, Song Tang, Qingdu Li, Shouming Zhong. A new 4D hyperchaotic system with high complexity, Mathematics and Computers in Simulation, 146 (2018): 44–56).

[0142] The structure of this hyperchaotic four-dimensional system is as follows:

[0143]

[0144] From formula (9), we can see that the system contains four variables (x, y, z, w), and its time series (x n ,y n ,z n ,w n ).

[0145] 1.2) Determine the desired parameters, the order of solving the optimal parameter values ​​and the given parameter values ​​based on the selected system structure.

[0146] It can be seen from formula (9) that the system contains a total of seven parameters, namely [abcdefr]. The system takes a set of values ​​when it is in a hyperchaotic state, namely [abcdefr] = [80 45 22 5 21 8 100]. The present invention uses this set of values ​​as the initial values ​​of the system parameters. The current parameter to be solved is determined to be a, and the order of solving other parameters is b, c, d, e, f and r. In the process of finding the optimal value of parameter a, the values ​​of parameters b~r remain unchanged; when the optimal value of the parameter a is found, the optimal value is used to update the initial value of the parameter to be solved 80.

[0147] 1.3) LE value and dissipative system analysis.

[0148] The four LE values ​​of the hyperchaotic four-dimensional system have been obtained in the literature [1], which are:

[0149] L E1 =25.6206,L E2 =11.2401,L E3 =1.717e-5,LE4 =-115.0336,

[0150] The four LE values ​​satisfy L E1 >L E2 >L E3 >L E4 , the literature [1] also analyzed the conditions that the system must satisfy for a chaotic system to be a dissipative nonlinear dynamic system:

[0151]

[0152] Right now:

[0153] Because the two largest LE values ​​are greater than 0, and the system also satisfies the condition that a chaotic system must be a dissipative nonlinear dynamic system (10), the hyperchaotic system in reference [1] is in a hyperchaotic state under the current parameter [abcdefr] = [80 45 22 5 218 100].

[0154] Due to L E3 The value is about 0, L E4 The value is negative and too small, which is consistent with L E1 and L E2 The values ​​of L are too far apart, and the hyperchaotic characteristics of the system are mainly affected by L E1 and L E2 Therefore, this paper only studies the positive L E1 and L E2 The two LE values ​​are very large, both exceeding 10, so the present invention calls this system a system with a large LE value. A hyperchaotic system with a large LE value has strong chaotic and random characteristics. On this basis, by selecting the optimal values ​​of the seven parameters, the L E1 and L E2 The value of can be used to improve the randomness and stability of the hyperchaotic system.

[0155] 2) Time series solution and stability analysis of hyperchaotic four-dimensional system variables.

[0156] 2.1) According to the fourth-order Runge-Kutta formula (1) and the given seven parameter values, the discretization parameters in the hyperchaotic system are calculated as follows:

[0157]

[0158] Finally, the time series (x, y, z, w) of the four variables (x n ,y n ,z n ,w n )for:

[0159]

[0160] Formula (11) is the iterative formula of the chaotic system variables derived from the discretized parameters. Here, Δt = 1 and h = 0.01 are taken. Based on the given system initial values ​​(x0, y0, z0, w0) and seven parameter values, the iterative trajectory (x0, y0, z0, w0) of the hyperchaotic four-dimensional system in the literature [1] at any time n can be obtained. n ,y n ,z n ,w n ) and a time series consisting of n iterative trajectories.

[0161] 2.2) Analyze and compare the performance of variables under stable and abnormal conditions based on the time series obtained in step 2.1).

[0162] According to step 2.1), the time series of the four variables in the hyperchaotic four-dimensional system under the given parameter values ​​are obtained, and its time series diagram and phase plane diagram are drawn as follows: Figure 4 and 5 As shown. Figure 4 It can be seen that each variable in the system fluctuates around a center and changes randomly, which means that the system has randomness, that is, sensitivity to the initial value. Figure 5 It can be seen that the system has hyperchaotic attractor characteristics, and the trajectory distribution characteristics in the operation space are good, ergodic and dense. Figure 4 and Figure 5 It is the time series and phase plane diagram of the normal change of variables. Because of the randomness of chaotic systems, although the time series of chaotic variables at each parameter value and each moment are different, the change rules under normal conditions are the same. Figure 4 and 5 Similarly, when the variable operation is abnormal, although the system is still in a hyper-chaotic state, the performance has changed significantly, such as Figure 6 and 7 shown. Figure 6 The changes in the variables in the second half of the time series deviate from the original track and change randomly, making Figure 7 The phase plane shape in the data has undergone an abnormal change, that is, the trajectory distribution characteristics of the variable have been destroyed. Therefore, the present invention uses the sample standard deviation method in step 4) to determine the discreteness of the variable, thereby determining whether the variable has undergone an abnormal change.

[0163] 3) Ensure that the system remains a hyperchaotic system within the range of the required parameters.

[0164] In step 1), it is determined that parameter a among the seven system parameters [abcdefr] is the currently required parameter.

[0165] 3.1) Determine the initial value range of parameter a.

[0166] In step 1), the classical value of a in the literature [1] is 80. An initial value range of a∈[40,120] is determined around it, and the values ​​of other parameters remain unchanged. The change characteristics of the two maximum LE values ​​within the value range are analyzed.

[0167] Use formula (2) to calculate the two maximum LE index values ​​in the range of a∈[40,120] and draw the corresponding LE index spectrum, as shown in Figure 8 shown. Figure 8 The upper curve is L E1 , the curve below is L E2 From the figure, we can clearly see two characteristics: First, the two LE indices change dramatically near a = 60, and L E2 The sequence has a value less than 0, so when the parameter a takes this position, the hyperchaotic four-dimensional system in the literature [1] is no longer a hyperchaotic system; second, the two LE values ​​increase in the direction of increasing parameter a. Therefore, according to the greedy strategy, the optimal value of parameter a should be searched in the direction of increasing LE value, which can improve the search speed.

[0168] 3.2) Adjust the value range of parameter a.

[0169] Remove the values ​​of a and their adjacent areas corresponding to the negative LE values ​​in the range of a∈[40,120] obtained in 3.1), and then adjust the value range of parameter a in the direction of increasing LE value according to the greedy strategy. In summary, the value range of parameter a is adjusted to a∈[70,120], and the adjusted exponential spectrum results are as follows Figure 8 As shown, all LE values ​​in the graph are positive.

[0170] 4) Determine the stability of the variables of the hyperchaotic four-dimensional system within the range of the desired parameter values, and continue to adjust the range of the desired parameter values ​​based on the determination results.

[0171] The sample standard deviation method is used to determine the stability of hyperchaotic system variables within the range of parameter a∈[70,120].

[0172] 4.1) Sampling parameter a takes the time series X of four variables under 40 normal states and 10 abnormal states i =(x i ,y i ,z i ,w i ),i=1,...,40;X j =(x j ,y j ,z j ,w j),j=1,...,10;

[0173] Here, 40 time series of variables under normal conditions in the interval of parameter a∈[50,200] are sampled as sample test values. The values ​​of parameter a corresponding to the serial values ​​of normal variables Serial Number (1~40) are: [50 55 65 70 7578 80 85 9092 95 100 105 108 110 113 115 120 123 125 130 135 138 140 145 150152 155 160 165 168 170175 178 180 182 185 190 195 198]. The abnormal variables sample 10 values ​​in a∈[200,240]. The parameter a values ​​corresponding to the Serial Number (1 to 10) of the abnormal variables are: [215 217 220 221 222 223 229 230 231 232].

[0174] According to formula (11) and the discretization parameters, the time series X of the four variables at each value is obtained. i =(x i ,y i ,z i ,w i ),i=1,...,40;X j =(x j ,y j ,z j ,w j ),j=1,...,10.

[0175] 4.2) According to formula (3), calculate the mean of the time series of parameter a under 40 normal values ​​and 10 abnormal values ​​in step 4.1) and

[0176] 4.3) According to formula (4) and steps 4.1) and 4.2), calculate the sample standard deviation σ of parameter a under 40 normal and abnormal values ​​in step 4.1) respectively. k ;

[0177] 4.4) The parameter a obtained in step 4.3) is used to calculate the average value of the standard deviation of the 40 samples under normal conditions in 4.1) according to formula (4). As a comparison value;

[0178] 4.5) Use formula (4) to find the value of σ for parameter a at a certain test value.

[0179] σ under 40 normal states and 10 abnormal states in step 4.1) k The value has been calculated in step 4.3) and does not need to be calculated again here; if the value of parameter a is not within this range, it needs to be calculated again.

[0180] 4.6) According to formula (5) and steps 4.3) and 4.4), calculate the sample standard deviation ratio K of parameter a under 40 normal states and 10 abnormal states in step 4.1). σ , respectively denoted as Kx, Ky, Kz and Kw, such as Fig. 9 and 10 As shown in the two figures, it can be seen that K σ The value is much larger than the value in the normal state. In order to make the comparison obvious, they are compared under the same coordinates, such as Fig.11 shown.

[0181] In the figure, the “*” line “Normal” indicates the K σ The “◇” line “Abnormal” represents the K value under abnormal conditions. σ The dashed line above represents the K of the 10 outlier variables. σ Minimum K σ_n_min , the dotted line below represents the K of 40 normal sample variables σ The maximum value K σ_abn_max .from Fig.11 It can be seen that the K of each variable σ The values ​​vary greatly.

[0182] 4.7) Set the threshold K of the sample standard deviation ratio th .according to Fig. 9 The ratio of the sample standard deviation under normal conditions in the four variables is slightly greater than the maximum value of the sample variable. The four variables are (Kx'Ky'Kz'Kw') = (0.1 0.250.30.15). According to the K obtained in step 4.6) σ_n_min and K σ_abn_max value, determine the K of each threshold th They are twice or more of the maximum value respectively, that is, (Kx_th Ky_th Kz_th Kw_th) = (0.2 0.5 0.6 0.3).

[0183] Test a∈[70,120] range, K of each variable σ Does the value satisfy K σ <K th , if yes, it means that the chaotic system variables change stably within the interval, that is, they are running on the normal track; otherwise, it is an abnormal state.

[0184] like Fig.12 As shown in the figure, the K values ​​of the four variables are obtained according to formulas (2) to (5) when the parameter a∈[70,120]. σ Serial Number 1 to 50 correspond to the 50 integer values ​​of parameter a from 70 to 120, and the dotted line above corresponds to the threshold value K of each variable. th , each "*" corresponds to each K σ As can be seen from the figure, each K σ The values ​​are all less than the corresponding threshold K th , so the system variables are stable in the interval a∈[70,120].

[0185] 5) According to the greedy strategy, the value range of parameter a is further adjusted in the direction of increasing LE index. After adjustment, it is a∈[120,220], and the stability of the system within this interval is determined.

[0186] 5.1) According to formula (1), calculate the LE index within this range and redraw the adjusted LE index spectrum, such as Fig.13 As shown in the figure, it can be seen that both LE indexes are positive, which meets the hyperchaotic system conditions.

[0187] 5.2) According to formulas (2) to (5), find K of the four variables a∈[120,220] σ Value, the result is Fig.14 As shown in the figure. Serial Number 1 to 100 correspond to 100 integer values ​​of parameter a from 121 to 220. As can be seen from the figure, when parameter a∈[120,200], the system is always in the stable region; starting from a=201, the system enters the unstable region, with a small amount of stable values ​​in the middle, so this part of the region is removed. Therefore, the optimal value of parameter a is in the stable region a∈[120,200].

[0188] 6) In the determined stable interval a∈[120,200], according to formulas (7) to (8), the optimal value of parameter a is obtained as a LE =193, where L E1 The value is approximately 46.5819, which is the maximum LE value obtained by the system when parameter a takes the optimal value.

[0189] 7) Update the initial parameter value of the original system with the currently obtained optimal parameter a value, and then sequentially obtain the optimal values ​​of other parameters b, c, d, e, f and r. That is, [abcdefr] = [80 45 22 5 21 8 100] is updated to [abc de fr] = [193 45 22 5 21 8 100].

[0190] According to the steps of finding the optimal value of parameter a, the optimal values ​​of other parameters are b LE =45, c LE =21,d LE =6,e LE =50,f LE =8,r LE =109, which corresponds to the maximum value of the system LE. The maximum value is to find the optimal value of the last parameter r LE =109, such as Fig.15 When all parameters take the optimal value, both LE values ​​are much larger than 0 and satisfy the condition of dissipative nonlinear dynamic system in formula (9):

[0191]

[0192] Therefore, under the optimal values ​​of the seven parameters, the hyperchaotic four-dimensional system is in a hyperchaotic state. This combination of parameter values ​​significantly improves L E1 and L E2 The value of .

[0193] Before parameter adjustment, from step 1), we can see that the two maximum LE values ​​are L E1 =25.6206,L E2 =11.2401; after adjustment, we get L E1 =75.7936,L E2 =71.2260, which is much larger than the value before adjustment. Therefore, this parameter selection method greatly improves the randomness and stability of the hyperchaotic four-dimensional system in the literature [1].

[0194] The present invention improves the LE value of the hyperchaotic four-dimensional system, thereby improving the randomness of the hyperchaotic four-dimensional system.

[0195] An electronic device provided by an embodiment of the present invention includes a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the device is running, the processor communicates with the memory through the bus, and the processor executes the machine-readable instructions to perform the steps of the method for selecting the optimal values ​​of any hyperchaotic four-dimensional system parameter as described above.

[0196] Specifically, the above-mentioned memory and processor can be general-purpose memory and processor, which are not specifically limited here. When the processor runs the computer program stored in the memory, it can execute the above-mentioned method for selecting the optimal values ​​of the hyperchaotic four-dimensional system parameters.

[0197] Those skilled in the art will appreciate that the structure of the electronic device does not limit the electronic device and may include more or fewer components than shown in the figure, or combine or split certain components, or arrange the components differently.

[0198] In some embodiments, the electronic device may also include a touch screen that can be used to display a graphical user interface (e.g., a startup interface of an application) and receive user operations on the graphical user interface (e.g., startup operations on an application). The specific touch screen may include a display panel and a touch panel. The display panel may be configured in the form of LCD (Liquid Crystal Display), OLED (Organic Light-Emitting Diode), etc. The touch panel may collect the user's contact or non-contact operations on or near it, and generate pre-set operation instructions, for example, the user uses any suitable object such as a finger, stylus, or accessories on or near the touch panel. In addition, the touch panel may include two parts: a touch detection device and a touch controller. Among them, the touch detection device detects the user's touch orientation and posture, detects the signal brought by the touch operation, and transmits the signal to the touch controller; the touch controller receives the touch information from the touch detection device, converts it into information that the processor can process, and then sends it to the processor, and can receive and execute commands from the processor. In addition, the touch panel can be implemented by various types such as resistive, capacitive, infrared and surface acoustic wave, and any technology developed in the future can also be used to implement the touch panel. Further, the touch panel can cover the display panel, and the user can operate on or near the touch panel covered on the display panel according to the graphical user interface displayed on the display panel. After the touch panel detects the operation on or near it, it is transmitted to the processor to determine the user input, and then the processor provides corresponding visual output on the display panel in response to the user input. In addition, the touch panel and the display panel can be implemented as two independent components or integrated.

[0199] Corresponding to the method for starting the above-mentioned application, an embodiment of the present invention further provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for selecting the optimal values ​​of any hyperchaotic four-dimensional system parameter are executed.

[0200] The application startup device provided in the embodiment of the present application can be specific hardware on the device or software or firmware installed on the device. The device provided in the embodiment of the present application, its implementation principle and the technical effect produced are the same as those in the aforementioned method embodiment. For the sake of brief description, the parts not mentioned in the device embodiment can refer to the corresponding contents in the aforementioned method embodiment. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices and units described above can all refer to the corresponding processes in the aforementioned method embodiment, and will not be repeated here.

[0201] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0202] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of modules is only a logical function division. There may be other division methods in actual implementation. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0203] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0204] In addition, each functional module in the embodiments provided in the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0205] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0206] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0207] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0208] 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 above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system, characterized in that: The steps include: Step S1, selecting a hyperchaotic four-dimensional system with a large LE value and performing performance analysis to determine the parameters to be sought and their initial values ​​and the order in which the optimal values ​​of the parameters are sought; Step S2, solving the time series of the hyperchaotic four-dimensional system variables and performing stability analysis on the hyperchaotic four-dimensional system variables; Step S3, performing a hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system whose desired parameter is within the initial value range, and obtaining a hyperchaotic characteristic value range of the desired parameter when the hyperchaotic four-dimensional system is always in a hyperchaotic state; Step S4, judging the stability of the hyperchaotic four-dimensional system variable within the hyperchaotic characteristic value range of the desired parameter, if it is stable, proceeding to step S3, and continuing to adjust the value range of the desired parameter of the hyperchaotic system according to the greedy strategy; otherwise, narrowing the value range of the parameter, determining the final value range of the desired parameter when the hyperchaotic four-dimensional system variable is stable, and proceeding to step S5; Step S5, calculating the optimal value of the required parameter and the maximum LE value.

2. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to claim 1, characterized in that: The step S1 comprises the following steps: Step S11, selecting a hyperchaotic four-dimensional system with a large LE value from the hyperchaotic four-dimensional systems constructed in the existing literature; Step S12, determining the order of solving the required parameters, the initial parameter values ​​of the required parameters and the optimal parameter values ​​according to the selected hyperchaotic four-dimensional system structure; Step S13, analyzing the LE value and dissipativeness of the selected hyperchaotic four-dimensional system to ensure that it has two positive and large LE values.

3. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to claim 1, characterized in that: The step S2 comprises the following steps: Step S21, the selected hyperchaotic four-dimensional system with a large LE value is used to calculate the time series (x, y, z, w) of the four variables (x, y, z, w) in the hyperchaotic four-dimensional system according to the given parameter values ​​and the fourth-order Runge-Kutta formula. n ,y n ,z n ,w n ): Use the fourth-order Runge-Kutta formula to calculate the time series x of one variable x n , the formula is as follows: Among them, x is a variable in the hyperchaotic four-dimensional system, x n is the time series of variable x, f(·) is the structure of the selected hyperchaotic four-dimensional system, Δt is the sampling time, h is the iteration step, and the subscript n represents the number of iterations; Step S22, according to the obtained time series (x n ,y n ,z n ,w n ) Analyze the performance of variables under stable and abnormal conditions to determine the causes of abnormal conditions.

4. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to any one of claims 1 to 3, characterized in that: The step S3 comprises the following steps: Step S31, determining an initial value range of the desired parameter with the initial value of the desired parameter as the center, calculating two positive LE indexes within the initial value range by using the time series of the hyperchaotic four-dimensional system variables, and drawing the LE index spectrum; Step S32, according to the obtained parameter L at each value E1 and L E2 The value is judged, the parameter value corresponding to the negative LE value is eliminated, and then the value range of the parameter p is readjusted in the direction of increasing the LE value according to the greedy strategy. min and p max ; Ensure that the two LE values ​​are always positive within the parameter value range, that is, the system is always in a hyperchaotic state.

5. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to claim 4 is characterized in that: The step S31 comprises the following steps: Assume that the current parameter is p, the initial parameter value is p0, and determine a value range p∈[p min ,p max ], satisfying p min <p0<p max , calculate p∈[p according to the LE value calculation formula min ,p max ], the two largest LE indices with integer values ​​of parameter p are denoted as L E1 and L E2 , and draw the corresponding LE index spectrum to observe L E1 and L E2 The values ​​in this range must satisfy that both sequence values ​​are positive numbers. The LE value calculation formula is: Among them, △D0 is the length of the two initial values, △D i is the distance between the i-th variables, i=1~n; In p∈[p min ,p max Each LE value of the system within the range of ] needs to be calculated N size Index, N size =p max -p min , is L E1 and L E2 Length; In the hyperchaotic four-dimensional system, take two very close initial values ​​X0 and X0' of the variables, X0 = (x0, y0, z0, w0), X0' = (x0', y0', z0', w0'), and calculate two sample sequences X of length n according to the two initial values ​​and formula (1). n and X n ', X n =(x n ,y n ,z n ,w n ), X n '=(x n ',y n ',z n ',w n '); In the parameter p∈[p min ,p max ], a total of N size LE index.

6. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to claim 5, characterized in that: The step S4 comprises the following steps: Step S41: Take the variable time series X under N normal states and M abnormal states according to the required parameter p i =(x i ,y i ,z i ,w i ),i=1,...,N;X j =(x j ,y j ,z j ,w j ),j=1,...,M; Step S42, find the mean of the variable time series under each value of parameter p and Step S43, respectively calculate the sample standard deviation σ of parameter p under N normal states and M abnormal states k and σ k ': Where n is the length of each variable time series; Step S44: taking the average value of the sample standard deviation of parameter p under N normal conditions as the comparison value Step S45, using formula (4) to calculate the σ value of parameter p under the test value; Step S46, calculate the sample standard deviation ratio K σ : Step S47: according to the sample standard deviation ratio K of the variable under normal state and abnormal state, σ The difference between the two sets of samples sets the threshold K of the sample standard deviation ratio. th , if K σ <K th , it means that the chaotic system variables change stably, that is, it is running on the normal track; otherwise, it is an abnormal state; Step S48: If the chaotic system variables change stably, go to step S3 and continue to adjust the value range of the parameters required by the hyperchaotic system according to the greedy strategy; if the chaotic system variables change to an abnormal state, narrow the value range of the parameters, determine the final value range of the parameters required when the hyperchaotic four-dimensional system variables are stable, and go to step S5.

7. The method for selecting the optimal value of the hyperchaotic four-dimensional system parameter according to claim 6, characterized in that: The step S5 comprises the following steps: Step S51: according to the final value range of the parameter to be sought, E1 Find the maximum LEmax and its location LEmax_id: [LEmax, LEmax_id]=max(L E1 ) (7); Step S52, obtain the maximum L E1 The value of parameter p LE : Then the final p LE The value is the optimal value of parameter p that can enable the system to obtain the best randomness.

8. A device for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system, characterized in that: include: The system selection and analysis module is used to select a hyperchaotic four-dimensional system with a large LE value and perform performance analysis to determine the parameters and their initial values ​​and the order of solving the optimal parameter values; The time series solving module is used to solve the time series of the hyperchaotic four-dimensional system variables and to perform stability analysis on the hyperchaotic four-dimensional system variables; A hyperchaotic characteristic analysis module is used to analyze the hyperchaotic characteristics of a hyperchaotic four-dimensional system whose parameters are within an initial value range, and obtain a hyperchaotic characteristic value range of the parameters when the hyperchaotic four-dimensional system is always in a hyperchaotic state; The stability judgment module is used to judge the stability of the hyperchaotic four-dimensional system variables within the hyperchaotic characteristic value range of the required parameters. If the hyperchaotic four-dimensional system variables are stable, the hyperchaotic characteristic analysis module is used to perform hyperchaotic characteristic analysis on the hyperchaotic four-dimensional system with the required parameters within the initial value range, and the value range of the required parameters of the hyperchaotic system is adjusted according to the greedy strategy; otherwise, the value range of the parameters is reduced to determine the final value range of the required parameters when the hyperchaotic four-dimensional system variables are stable. The optimal value calculation module is used to calculate the optimal value of the required parameter and the maximum LE value.

9. An electronic device, characterized in that: It includes a processor, a memory and a bus, the memory stores machine-readable instructions executable by the processor, when the electronic device is running, the processor and the memory communicate through the bus, and the processor executes the machine-readable instructions to perform the steps of the method for selecting the optimal values ​​of the hyperchaotic four-dimensional system parameters as described in any one of claims 1-7.

10. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by a processor, executes the steps of the method for selecting optimal values ​​of parameters of a hyperchaotic four-dimensional system as described in any one of claims 1 to 7.

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