Function Synchronizations of Dynamic Systems

In this chapter, the function synchronization of the controlled Duffing oscillator with van der Pol system and pendulum system is studied. Based on the theory of discontinuous dynamical systems, the analytical conditions for chaos synchronization of three different systems are obtained under sinusoidal constraints. With these conditions, the control parameter maps and the synchronization invariant sets are derived, respectively. Numerical illustrations for partial and full combination synchronization among three systems are carried out.