Boundness On Chaotic Systems With Its Control And Synchronization

Chaotic dynamics is a new subject, chaotic itself is unstable, it is sensitive to the initial value. A chaotic attractor is ensured by two things, one is that the system has a trapping region which guarantees the existence of an attractor, and the other is that the system displays chaotic behavior on the attractor. According to construct a proper Lyapunov function, the paper solves the problem of the boundness of T system, fractional-order financial system and NSG system.The theoretical results of the boundedness of chaos systems can be used for chaos control, effective linear feedback controller was proposed for stabilizing chaos to unstable equilibrium (0,0,0) , linear feedback control to achieve synchronization in bounded dynamic systems are studied. Numerical simulations results are presented to demonstrate the effectiveness of the proposed method.