Chaos Synchronization Based On Impulsive Control And Its Application In Secure Communication

Chaos synchronization is important and useful in applied physics, electronic engi-neering, and biological sciences. In practical implementation of chaos synchronization systems, Since the dynamic response of chaotic system is highly sensitive to the initial values of a system and the variation of a parameter, and chaotic trajectory is so unpre-dictable, Chaotic systems are able to be assumed this important task due to its natural. Now it is urgent to create a new encryption mechanism, the application of chaotic system for communication encryption and decryption is unequivocally valued.In this dissertation, Chaos synchronization, that is the several key issues in chaotic secure communication are researched and chaos-based communication schemes are proposed as well, which are detailed as follows:First, the dissertation discusses systematically basic concepts of chaos:definition, main feature, the significance and the respect of chaos are investigated briefly. After that we introduce some elementary theories:Lyapunov exponent reflectioning chaos dynamics characteristic, research chaotic system synchronization needs the structure Lyapunov function, Lyapunov stability theory and so on and analysis the Fixed-Time system, Time-Delay chaotic system.Second, in part of impulsive synchronization design and laws, we have considerde the problem of impulsive control based on the theory of impulsive differential equa-tions. Some sufficient conditions were derived to ensure the asymptotic stability of an impulsive differential system. The result are also applied to design an impulsive control for a class of nonlinear systems. We also present a theory of impulsive synchronization of two chaotic systems. A linear impulsive feedback synchronization rule is proposed according to synchronization errors. The condition of synchronization of synchroniza-tion asymptotic stability of the rule; Namely, an estimation of the impulsive interval is given. Simulation results based some typical chaotic systems, that is Lorenz, Chua, unified chaos systems, are provided. to show the performance; Simulation results are given to demonstrate the performance of the proposed scheme.Finally, we design a scheme for communication system security based on the study above. With the scheme, message signals are not transmitted across public channels, but induced at the receiver end. The scheme overcomes the transmission time-frame congestion in impulsive cryptosystems discussed in the literature and improves system security.