一个复杂混沌系统的分析与同步控制

Analysis and Synchronization Control of a Complex Chaotic System

为了更好研究混沌现象的本质和利用混沌,根据混沌系统的李雅普诺夫稳定性理论和分岔理论研究了一类三维广义Rabinovich系统的混沌动力学特性,包括耗散性、平衡点和局部渐近稳定性、李雅普诺夫指数、李雅普诺夫维数、分岔图、全局吸引域等.依据混沌系统全局指数吸引集的结果和Dini导数,设计合适的控制器实现了两个相同混沌系统的全局指数同步.为了使所设计的控制器在实际应用中更容易实现且使同步方案有高效的同步速率,文章设计了线性反馈控制器使两个混沌系统达到全局指数同步.文章的创新点在于,首先得到了该混沌系统每个变量最终界的数学表达式,然后利用混沌系统的有界性得到了混沌系统控制器的精确数学表达式.最后,文章对同步过程进行数值模拟,仿真结果证实了理论的可行性.

In order to study the nature of chaos and make use of chaos better,chaos in a three-dimensional generalized Rabinovich system is studied in this paper according to Lyapunov stability theory and bifurcation theory,including dissipation,the equilibrium point and local asymptotic stability,Lyapunov exponent,Lyapunov dimension,bifurcation diagram,global attractive domain,etc.According to the result of global exponential attractive set of this chaotic system and Dini derivative,a suitable controller is designed to realize global exponential synchronization for two identical chaotic systems.A linear feedback controller is designed to achieve global exponential synchronization for two identical chaotic systems in order to make it easier to achieve fast synchronization for chaos synchronization scheme in practical applications.The innovation of this paper is that the boundedness of the chaotic system is obtained firstly,then the precise mathematical expression of the controller of this chaotic system is obtained by using the boundedness of this chaotic system.Finally,the numerical simulation of the synchronization process is carried out and the simulations confirm the feasibility of the theoretical results.