Coexistence of complete-synchronization and anti-synchronization for uncertain chaotic systems via adaptive control

This letter studies the coexistence of complete-synchronization and anti-synchronization (hybrid synchronization) for a general class of uncertain chaotic system. A simple adaptive feedback scheme is proposed to achieve the hybrid synchronization, and identify the unknown parameters that chaotic system function is an odd function when it is anti-synchronization. The stability of the error systems are analyzed based on Lyapunov stability theory. 4D non- autonomous Qi system and 3D autonomous Rössler system are successfully applied to achieve the hybrid synchronization and parameters identification. Numerical results are presented to justify the effectiveness and feasibility of the method.