Impulsive Adaptive Synchronization And Control Of Several Hyperchaotic Systems

Chaos widespread in nature and have been attracted more and more people to studyit. In recent years, people continue to try to control the chaotic system in order to makechaos produce what people want and serve mankind. In this paper, we mainly studiedthree systems: hyperchaotic Lorenz system, hyperchaitic Chen system and hyperchaoticR ssler system, which based on adaptive control method, impulsive control theory andinvariant set stability theorems. We have drawn the following conclusions:(1) We study the Self-synchronization problems of hyperchaotic Lorenz system,Firstly, we analyze the dynamic behavior of the hyperchaotic Lorenz systemï¼›Secondly,by using the impulsive control method we formulate two simple controllers to controlthe system to its unstable and consider the case when the time intervals is equal andcontrol matrix is a diagonal matrixï¼› Finally, numerical simulations with Matlab arepresented to show the availability of our design.(2) Based on the invariance principle of impulsive different equations we study theSynchronization between two different systems: hyperchaotic Chen system andhyperchaotic R ssler system. We design a impulsive-adaptive controller to makes thehyperchaotic Chen system and hyperchaotic R ssler system to achieve synchronizationstatus. Finally, we use the numerical simulation to compare the effects betweenimpulsive-adaptive controllers with simple adaptive controller. We can easily see fromthe image that both methods can make the two systems to achieve synchronization, butcompared with the adaptive control, impulsive-adaptive control for synchronizationtime is shorter, higher efficiency.