The Combination Synchronization Of Chaotic Systems And Its Application In Secure Communication

In the usual drive-response synchronization model, there are one drive system and one response system, which can been seen as one-to-one system. Thus a natural and interesting question is:does the synchronization happen between two drive systems and one response system? This question deserves investigation for the secure communication, for example, in order to ensure that the transmission signals have strong anti-attack ability and anti-translated capability we can split the transmission signals into several parts, each part loaded in different drive systems, or divide time into different intervals, the signals in different intervals loaded in different drive systems. In this thesis, we first propose a new type of synchronization which have two drive systems and one response system, we refer this type of synchronization as combination synchronization. Then we investigate the combination synchronization of chaotic systems and its application in secure communication. This thesis is categorized into five parts and the organization is as follows.In the first chapter, some typical definitions of chaotic synchronization and methods commonly used in chaotic synchronization are introduced, also, the main contents of this paper are briefed.In the second chapter, we first generalize the usual drive-response synchronization model, which have one drive system and one response system, to the combination synchronization. Then we investigate the combination synchronization of three classics chaotic systems:Lorenz system, Chen’s system and Lu system by using active backstepping method, some sufficient conditions for combination synchronization are derived based on the Lyapunov theory. The numerical simulations are presented to verify the effectiveness of the proposed method.It is well known that in practical situations it is hard to exactly determine the values of the parameters of the chaotic systems in advance. Moreover, due to un-modeled dynamics, structural variations of the system and environment noises there are always some unknown model uncertainties and external disturbances in the chaotic systems. These uncertainties may cause system performance degradation and thereby destroy the synchronization. Therefore, investigation of the chaos synchronization between two uncertain chaotic systems is an important research issue. So, in the third chapter, the adaptive control technique is adopted to synchronize three different chaotic systems with parameter and model uncertainties and stochastic perturbation in finite time. A general scheme and parameters update laws are developed to deal with stochastic perturbed combination synchronization for three different chaotic systems. The simulation results show the feasibility of the proposed method.Based on the results proposed in the above chapter, the forth chapter addresses the application of combination synchronization in secure communication. The transmission signal is split into two parts, each part loaded in the Lorenz drive system and Chen’s drive system, respectively. The Lu system is the response system which receives the signals transmitted by two drive systems. A novel sufficient condition is obtained to ensure combination synchronization and the numerical simulations are also given to show the feasibility of the proposed method.In the fifth chapter, the research work of this thesis is summarized and the possible direction is further proposed.