Research On Chaotic And Hyperchaotic Systems With Different Families Of Attractors And Their Synchronous Control

Chaos,the inherent randomness of deterministic systems and a unique form of non-linear dynamic systems,widely exists in nature.Many scholars have continuously improved Lorenz's work and obtained many classical chaotic systems since Lorenz discovered the first chaotic attractor.However,the dynamic behaviors of these chaotic systems are relatively simple,and their applications in secure communications are not effective.Therefore,the research and discovery of chaotic and hyperchaotic systems with complex dynamic behavior have become a hot research topic in recent years,and hidden attractors have attracted much attention due to their complex dynamic behaviors.At present,the research of chaotic and hyperchaotic systems with hidden attractors have achieved some results,but most of them only focus on a class of hidden attractors.The research on chaotic and hyperchaotic systems with multiple types of hidden attractors or multiple types of hidden attractors and self-excited attractor are still in the primary stage,and there is space for further development and improvement.Based on this,the chaotic and hyperchaotic systems with different families of attractors are studied in this thesis.The main works are as follows:1.A three-dimensional continuous autonomous chaotic system with different families of attractors is proposed and analyzed.A hardware analog circuit and an adaptive synovial controller of the system are designed and simulated.Firstly,the dynamic behaviors of the system are studied by time series diagram,phase diagram,Lyapunov exponential spectrum and bifurcation diagram,and it is found that:(1)With the change the system parameters,the system has an unstable equilibrium point,no equilibrium,infinite equilibrium point and a stable equilibrium point while maintaining chaotic dynamic behaviors,which indicates that the system has self-excited attractor and three kinds of hidden attractors;(2)the system is always in chaotic state with a wide range of parameter;(3)by changing the initial conditions of the system,the system has the coexistence of attractors,including chaotic attractor and periodic attractor,and different periodic attractors.In addition,according to the theory of topological horseshoe and numerical calculation,the topological horseshoe of the system is found,and the topological entropy is obtained.Then,the hardware analog circuit of the system is designed and simulated with Multisim.The simulation results verify the dynamic characteristics of the system and show the realizability of the system.Finally,based on Lyapunov stability theory and synovial control method,an adaptive synovial controller is designed.The simulation results show that the controller can track the position signal quickly and accurately.2.A four-dimensional hyperchaotic system with different families of attractors is studied and analyzed.The hardware analog circuit and adaptive synchronization controller of the system are designed and simulated.Firstly,the dynamic behaviors of the system are analyzed and it is found that:(1)By choosing appropriate parameters,it is found that there exists an unstable equilibrium point,no equilibrium,infinite equilibrium point and a stable equilibrium point while maintaining hyperchaotic dynamic behaviors;(2)There are many kinds of attractors coexisting in the system,including hyperchaotic attractor and periodic attractor,chaotic attractor and point attractor,and complex transient hyperchaotic behavior is shown under certain initial conditions.Then,the hardware analog circuit of the system is designed and simulated with Multisim.The simulation results verify the existence of the coexistence attractors and the realizability of the system.Finally,based on Barbalat theorem and Lyapunov stability theory,an adaptive synchronization controller is designed to realize the adaptive synchronization of the system.