Synchronization for a class of nonlinear nonautonomous vibration system

For a class of nonlinear nonautomonous vibration system, a novel method for constructing a derived system to reach synchronization with the original system is presented and verified. There exists two parts in control terms of the derived system, one is a constant matrix, the another is a function matrix. The constant matrix is used to make the trivial solution of linear part of difference function asymptotic ally stable. The function matrix is employed to transform the nonlinear part into a power function, which warrants the synchronization between the original and the derived system. For a Mathieu system excited by parameters and external force, the simulation is carried out to show that the responses of the original and the derived system can reach identical eventually. For a Φ⁶-Duffing system, the simulation results show that the two responses reach identical after a short time.