Projective Synchronization For Different Hyperchaotic Systems Based On Adaptive Control Method

With the interdisciplinary and integration of modern science, chaos science hasbroken the barriers between disciplines, and shifted from purely theoretical researchto practical application. More and more actual and potential applications of chaoshave been widely discovered, especially in secure communications, chaos has animmeasurable potential. In the meanwhile, chaos synchronization technology israpidly developing, which provides new methods for secure communicationapplications.This article proposed two adaptive projective synchronization schemes fornon-identical hyperchaotic chaotic systems. Several technologies and means toachieve chaos synchronization have been analyzed, and advantages and disadvantagesof these methods have been summarized. Based on amounts of readings andresearches, this paper proposed several projective synchronization methods apply todifferent hyperchaotic system, the designed synchronization controllers are featuredwith high universality and feasibility. The main results of this paper are as follows:(1) A new generalized modified function projective synchronization scheme fordifferent chaotic system is proposed. The drive and response systems can besynchronized up to a desired scaling function matrix, which not only contains timevariables, but also has space variables. Combining Lyapunov stability theory andadaptive control theory, two more generalized controllers and adaptive parameter lawsare designed to realize the synchronization and anti-synchronization of twonon-identical hyperchaotic systems, respectively. Finally, synchronizations ofhyperchaotic CYQY system and hyperchaotic Chen system are simulated todemonstrate the effectiveness of this method.(2) A time-controllable exponential synchronization scheme for different chaoticsystem is proposed. Based on calculus and linear algebra, two general synchronizationcontrollers and parameter update laws are designed for systems with and withoutdisturbances，respectively. The drive and response systems can be synchronized up toa given scaling matrix at a pre-specifed exponential convergence rate. The innovativeof this method is that: in case of non-disturbance or weak disturbances, thesynchronization time is controllable simply by adjusting the controller parameters.All of the results in this paper are simulated on Matlab platform, and Runge-Kutta algorithm is applied. The experimental results are consistent withtheoretical expressions deduction. Comparing to latest works, the proposed designsare more creative and practical. The article also summarizes and compares theLyapunov stability theory and exponential stability theory, we have applied thesetheories to chaos synchronization, which lays the foundation for further study ofchaos synchronization.