Realizing hybrid synchronization of time-delay hyperchaotic 4D systems via partial variables

Hybrid synchronization of time-delay hyperchaotic 4D systems with different initial conditions is investigated via partial variables. Based on the Lyapunov stability theory, sufficient conditions are given to get the hybrid synchronization by constructing a novel Lyapunov function in the form of exponential form. It is proved that some partial state variables of two time-delay hyperchaotic systems are anti-synchronized, while other state variables are complete synchronized, when one or two linear controllers are imposed on the response system. Simultaneously, the unknown parameters in the response system are also estimated completely. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.