Chaos Synchronization With Different Structures And Implusive Synchronization Of Fractional-order System

The theoretical research on fractional-order calculus has been developed300years,however, the boom research of its application on engineering and physics has been onlyrose in the recent decades. Chaos control and chaos synchronization of fractional-orderdynamical systems are the focus on nonlinear field. Due to the larger key space infractional-order systems, and the fractional-order systems with different structures aremore common in the field of secret communication, and impulsive synchronization canimprove the confidentiality of chaos systems. Therefore, it has great significance tostudy chaos synchronization with different structures and impulsive synchronization offractional-order system.This article is based on the stability theory of the fractional-order system andLyapunov stability theory, using the methods of theoretical derivation and numericalsimulation to study synchronization with different synchronization and impulsivesynchronization of fractional-order chaotic systems. The main contributions of thisarticle are as follows:(1) We make a systematic introduction of the predecessors’ researches andinnovation, mainly including the concept and characteristics of chaos, the researchstatus of fractional-order chaotic systems at home and abroad, and methods offractional-order chaotic system synchronization.(2) We give the basic concepts and theorems of the fractional operators.(3) When the parameters are known, active control synchronization is adopted.Therefore, we can implement the synchronization between the fractional-orderhyperchaotic Chen system and the fractional-order hyperchaotic R ssler system. Finally,simulation results are obtained. This method is simple and effective.(4) When the parameters are unknown, a adaptive control law and a parameterupdate rule are introduced. And we can implement synchronization between responsesystem and drive system. Further validate the results of the different structuresynchronization through numerical simulation.(5) The study of impulsive synchronization problem of a4D autonomous system isbased on Lyapunov stability theory. For fractional-order systems, when theapproximation and the Laplace transform of the frequency domain have used, we canconvert the fractional-order chaotic systems into the integer-order chaotic systems. So the impulsive synchronization of the integer-order chaotic systems is investigated.Sufficient conditions for achieving stability in the error system are derived. Finally,numerical simulations are given to demonstrate the feasibility and effectiveness of theproposed scheme.