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A New Grid Sine Cavity Hyperchaotic Mapping System
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A super-chaotic and sinusoidal technology, applied in the field of nonlinear systems, can solve complex nonlinear phenomena and other problems, and achieve the effect of clear phase diagram and rich dynamic characteristics
Inactive Publication Date: 2019-01-25
湖南特思科智能科技有限公司
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However, in practical engineering applications, many physical systems are described by two variables or even multiple variables, making two-dimensional or even multi-dimensional discrete maps have more complex nonlinear phenomena than one-dimensional discrete maps
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Embodiment 1
[0051] A new grid sinusoidal cavity hyperchaotic mapping system, the construction of which includes the following steps:
[0052] The first step is to establish a sinusoidal discrete nonlinear function model based on closed-loop modulation coupling. For details, see figure 1 , to obtain the state equation of the m-dimensional control system, the specific process is as follows:
[0053] Step 1.1. Design an m-dimensional discrete-time system with a control parameter ω, specifically, expression 1):
[0054] X(n+1)=Af[x m (n),X(n+1),ω] 1);
[0055] Where: X(n)=[x 1 (n),x 2 (n),...,x m (n)] T , and satisfy m≥2; A is an m×m control matrix; f[x m (n), X(n+1), ω] is a uniformly bounded nonlinear feedback controller whose value is Expression 2):
[0056]
[0057] In expression 2) ω=[ω,ω,...,ω] T ;
[0058] Step 1.2, simplify expression 2) to get expression 3):
[0059] f i [x i (n),ω]=sin[ωx i (n)], i=1,2,...,m 3);
[0060] Step 1.3, take A as an expression 4) containin...
Embodiment 2
[0079] Combining the method of Example 1 to construct a two-dimensional sinusoidal cavity hyperchaotic mapping system, the details are as follows:
[0080] 1. The system equation of the unidirectional sinusoidal cavity is the expression 1-1):
[0081]
[0082] Among them: x and y are state variables, a is the amplitude, ω is the angular frequency, and c is the internal disturbance frequency. It is worth noting that: x n and y n are not zero, otherwise the system has no meaning, and x 0 and y 0 are not equal to kπ or
[0083] Set the initial value x(1)=0.3, y(1)=0.3, n=50000, under different value parameters, use Matlab to carry out numerical simulation, the chaotic attractor with unidirectional multi-sine cavity can be obtained as image 3 (a), image 3 (b), image 3 (c) and image 3 (d), where image 3 (a)-(d) are chaotic attractors under different parameters ( image 3 The abscissa and ordinate of (a)-(d) are x(n) and y(n) respectively), specifically: image 3...
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Abstract
The invention provides a novel grid sine cavity hyper-chaos mapping system. A construction method of the system includes following steps: step 1, building a sine discrete nonlinear function model based on closed-loop modulation coupling, and acquiring a state equation of an m-dimension control system; step 2, combining the state equation of the m-dimension control system acquired in the step 1 with a step wave function to acquire a state equation of the novel grid sine cavity hyper-chaos mapping system. Different amounts of one-dimension chaos attractors can be acquired by building the sine discrete nonlinear function model based on closed-loop modulation coupling and then changing system parameters; the sine discrete nonlinear function model is combined with the step wave function, the one-dimension chaos attractors are enabled to extend onto a plane to acquire grid hyper-chaos attractors, novel grid hyper-chaos mapping is constructed, and the attractors have clear phase diagrams and rich dynamic characteristics.
Description
technical field [0001] The invention relates to the technical field of nonlinear systems, in particular to a novel grid hyperchaotic mapping system. Background technique [0002] Existing chaotic maps can be divided into two categories: [0003] The first type, one-dimensional chaotic map, one-dimensional chaotic map has only a small number of parameters and one variable, such as Logistic map, Tent map, Chebyshev map and sinusoidal map. Its advantages are reflected in the implementation efficiency and simplicity of application. Therefore, they are widely used in cryptography and chaotic secure communication. But the complexity is low and the key space is small. With the development of the Internet and cloud computing, the one-dimensional chaotic map based on chaotic encryption can no longer guarantee the security of information transmission, because its orbit, parameters and initial conditions can be predicted by chaotic signalestimation technology. [0004] The second ...
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