Synchronization for a Unified Deformation Chaotic System Based on the Global Exponentially Attractive Set

On the basis of research on the effect of the chaotic system bounded by chaos synchronization and control, we propose a new synchronization method for chaotic systems based on the global attractive set. We get a unified deformation chaotic system by replaced the product term of the unified chaotic system with a quadratic one, and use the chaotic system as the system model. We solve the bounded problem of the unified deformation chaotic system and get the estimations of the ellipsoidal ultimately bounded set and positive invariant set correspondingly, which is applied to the chaotic synchronization by constructing a radically unbounded and positive definite Lyapunov function, and using linear control transformation method and Lagrange function. The diverse structure synchronization is realized between the unified and the uniform deformation chaotic systems by the designation of the right system controller to stabilize the error system of chaos synchronization at the original point. The proposed method is proved to be effective and accurate via the numerical simulations on boundary and different structures of the unified deformation chaotic system.