切换系统的建模、混沌反控制及其应用研究

As for continuous chaotic or hyperchaotic systems, most of which are determined by trial-and-error method involving numerical simulation and Lyapunov exponent calculation, there is not a general method at home and abroad by now. According to two fundamental theoretical issues in chaos anti-control of linear switching system and nonlinear switching system, this project makes some breakthrough in traditional trial-and-error numerical simulation, with Shilnikov theorem and establishing heteroclinic loop as starting point, concludes some general design criteria for chaos anti-control of linear and nonlinear switching system, proposes a novel method for chaotifying of switching system by combining anti-control principle, Shilnikov theorem and establishing heteroclinic loop in order to solve the general design problem related to chaos anti-control of switching system in theory, and build a type of switching chaotic and hyperchaotic system which will be further applied in the field of network multimedia security communication. The research on a general method for chaotifying switching system is both of important scientific significance and of application value in perfecting and developing chaotic theory.

对于大多数连续混沌或超混沌系统，目前国际上的研究方法及相关结果主要是通过试错法，在数值仿真以及计算李氏指数基础上获得的，未能找到一种较为通用的方法。本项目针对线性切换系统混沌反控制和非线性切换系统混沌反控制这两个基本理论问题，突破传统意义上研究混沌的数值实验层面上参数“试错法”存在的局限性，以Shilnikov定理和构造异宿环作为研究问题的切入点，建立线性与非线性切换系统混沌反控制的通用设计准则，提出将反控制原理和构造异宿环相结合的切换系统混沌化的建模新方法，最终从机理上解决切换系统混沌反控制的一般设计问题，建立一种基于切换系统反控制的混沌与超混沌吸引子体系，并在多媒体网络保密通信系统中获得应用。切换系统混沌反控制一般问题的研究对完善和发展混沌理论具有重要的科学研究意义和应用价值。

本项目针对线性切换系统混沌反控制和非线性切换系统混沌反控制这两个基本理论问题，突破传统意义上研究混沌的数值实验层面上参数“试错法”存在的局限性，以Shilnikov定理和构造异宿环作为研究问题的切入点，建立线性与非线性切换系统混沌反控制的通用设计准则，提出将反控制原理和构造异宿环相结合的切换系统混沌化的建模新方法，最终从机理上解决切换系统混沌反控制的一般设计问题，建立一种基于切换系统反控制的混沌与超混沌吸引子体系，并在多媒体网络保密通信系统中获得应用。切换系统混沌反控制一般问题的研究对完善和发展混沌理论具有重要的科学研究意义和应用价值。