Analysis Of Dynamical Behavior Characteristics Of Complex Continuous And Discrete Chaotic Systems

With the rapid development of the Internet,cloud computing,big data and other technologies,data security and user privacy protection are facing new challenges in the open network environment.Chaos is widely used in secure communication because of its sensitivity to initial state,ergodicity,inner randomness and unpredictability.However,with the development of chaos identification technology,chaotic systems with simple dynamic behavior are vulnerable to the attack of spectrum analysis and phase space reconstruction.Therefore,it is a challenging and valuable subject to study chaotic systems with complex dynamic behaviors.Chaotic systems can be divided into continuous system expressed by differential equation and discrete system expressed by state difference equation.Around these two kinds of systems,the construction of complex multiscroll chaotic systems and the cascading of arbitrary finite dimensional chaotic maps are discussed.In this dissertation,the modeling method,qualitative analysis and technical implementation of complex chaotic system are studied in depth,and some new phenomena and conclusions are given.The main research achievements are as followings:(1)Based on the classical Jerk system,a new multiscroll chaotic system is designed,which uses multi-level pulse signal to control the different shifts of the nonlinear function.The basic dynamic characteristics of the new system,such as equilibrium point distribution,phase diagram,Lyapunov exponent spectrum and bifurcation diagram,are analyzed in detail.Compared with the existing work,the dynamic behavior of the designed chaotic system is equivalent to the superposition of various attractor shapes under different shifts.Therefore,the designed chaotic system can realize multiscroll attractors with different scroll numbers and structures only by setting multi-level pulse signals.The circuit simulation shows that the number of scrolls can be adjusted by changing the external control signal,which simplifies the circuit implementation.(2)A general amplitude control method is proposed to construct multiscroll attractors by scaling partial or total state variables.In addition,a pulse control module circuit is designed to control the amplitude of state variables.According to the design criteria,two typical design examples are given,and the feasibility of this method is verified by circuit simulation.Compared with the existing work,the multiscroll chaotic system designed based on the proposed method can obtain various kinds of attractors,including nested attractors,axisymmetric attractors and centrosymmetric attractors,and the circuit implementation is simple.(3)A method of constructing complex chaotic system based on cascading of arbitrary finite dimensional isomorphic chaotic maps is proposed.The dynamic analysis shows that the Lyapunov exponent of the cascade system is equal to the sum of the Lyapunov exponents of each subsystem with disturbance.Therefore,by setting appropriate parameters,the cascade system has more advantages in obtaining robust chaotic and hyperchaotic systems.Taking the generalized Hénon map as an example,the dynamic properties of cascade system with different parameters and permutations are studied.The performance of the cascade system is evaluated from the aspects of Lyapunov exponent,bifurcation diagram,domain of attraction,and initial state sensitivity.Numerical simulation shows the effectiveness and practicability of this method.(4)On the basis of the research on the cascading of isomorphic chaotic maps,a modeling method of complex chaotic systems with heterogeneous chaotic maps cascading is proposed.The input and output domains of heterogeneous subsystems are normalized by introducing a sine function,and then cascade the normalized results.The proposed general framework provides great flexibility for the selection of subsystems.Chaotic maps with different dimensions and structures can be used as subsystems to generate a large number of new chaotic maps.Numerical simulation results show that the chaotic map has chaotic behavior in the whole parameter range and has robust chaotic characteristics.The design of complex chaotic system is the core of the application of chaotic system.Through the modeling of complex chaotic system,a series of improved chaotic systems are constructed,and the dynamic behavior of chaotic systems is analyzed,and its physical phenomena are revealed.The chaotic system designed in this paper has complex dynamic behavior,which can provide effective support for the further realization of secure communication.