Synchronization Of Chaotic Systems With Application To Secure Communication

Synchronization of chaotic systems and its application to secure communication has become a hot research topic in the field of nonlinear control.Based on the impulsive stability theory,practical stability theory,and Lyapunov stability theory respectively,the impulsive control and synchronization of chaotic Qi system,the impulsive practical synchronization of different hyperchaotic systems with uncertain parameters,the modified function projective synchronization of complex chaotic system,and its application to secure communication are discussed via combining the theoretical analysis and numerical simulation in this paper.The main contents of the paper are summarized as follows:1.Impulsive control and synchronization of chaotic Qi system.Based on the impulsive stability theory of dynamical differential equation,a class of impulsive control and synchronization of chaotic systems are studied by using impulsive control strategy,and some simple criteria is given and proved.We take chaotic Qi system as an example in numerical simulation,and the simulation results verify the effectiveness of the proposed scheme.2.Impulsive practical synchronization of different hyperchaotic systems with uncertain parameters.Based on impulsive practical stability theory,the impulsive practical synchronization of a class of different hyperchaotic systems with uncertain parameters is studied.Given impulsive error bound and appropriate impulsive control law,the upper bound of the impulsive interval can be estimated,and the algebraic criterion for realizing impulsive practical synchronization is obtained.We take four-dimensional hyperchaotic Chen and Lüsystem as examples to illustrate the feasibility of the method.The correctness and effectiveness of the theory is verified by numerical simulation.3.Impulsive practical synchronization of hyperchaotic systems with time delay and its application.We obtain some criteria to make different hyperchaotic systems with time delay and uncertain parameters realize practical synchronization via impulsive practical stability theory.And the impulsive interval can be estimated.We take hyperchaotic Lorenz and Chen system as example in numerical simulation,and the application of this synchronizationscheme to image secure communication is also presented.Simulation results further verify the effectiveness of this proposed synchronization scheme.4.The modified function projective synchronization of chaotic system in complex field and its application to secure communication.Based on the definition of synchronization and Lyapunov stability theory,response system is constructed with certain regularity and the complexity of designed controllers is greatly reduced simultaneously,then the modified function projective synchronization between drive and response systems can be achieved easily in the case of known and unknown parameters respectively,and secure communication scheme based on parameter modulation is established.Finally,numerical simulations with Matlab demonstrate the effectiveness and feasibility of the schemes of synchronization control and secure communication.