Synchronization control for chaotic systems based on adaptive method

Two kinds of synchronization control are proposed for chaotic systems with constant Lyapunov spectrum based on adaptive method. The first method can realize complete synchronization, anti-synchronization, projective synchronization and hybrid synchronization control, respectively. This method may be prove the validity by using the Lyapunov stability theory. The second method is adopted to design a special hybrid controller to achieve anti-synchronization, which includes two parts, which are pre-controller and feedback controller. The main characteristic of the second scheme doesn´t need to rely on the Ross-Hurwitz criterion and be suitable for the synchronization of high dimension chaotic system. Finally, numerical simulation is given to show the effectiveness of the proposed method.