Synchronization of a class of time-varied nonlinear vibration system

For a class of nonautonomous nonlinear vibration system, a corresponding derived system is constructed. A novel control method to realize the synchronization between the derived and the original system is presented. The method is proved by Lyapunov stability theory. The principle for choosing coupling parameters is given. For a Mathieu system excited by parameters and external force, the simulation is carried out. The result shows that the derived system can achieve fast synchronization with the original system under the action of chaos. The simulation for Duffing system excited by quasi-periodic force shows that the derived system can reach synchronization with the original system under the quasi-periodic motion.