Synchronization and anti-synchronization of chaos for a multi-degree-of-freedom dynamical system by control of velocity

For multi-degree-of-freedom dynamical systems, a novel control method was proposed to realize synchronization and anti-synchronization of chaos between the original and derived systems. The presented method was proved theoretically and realized by linear coupling of velocity. Furthermore, for any coupling coefficient larger than the critical value, the two systems can continue synchronization and anti-synchronization by the coupling method. This means that the synchronization and anti-synchronization can be kept within a wide range of coupling parameters. The simulation results for Duffing and Mathieu systems proved that the proposed method was correct and effective.