The coexistence of chaotic synchronization with three different nonautonomous systems under constraint conditions

Because of the inherent randomness and extreme sensitivity to initial values of chaotic systems, chaos synchronization has become the key technology for chaotic applications. With the further research, scholars have found that using continuous systems to simplify discontinuous systems cannot get accurate results, and it needs to use discontinuous models to provide a precise description. Therefore, the synchronization with three different chaotic systems will be studied by using discontinuous dynamical system theory in this paper. Taking Holmes–Duffing system as master system, Pendulum and the Stiffening Spring as slave systems, the motion laws of the three systems in different motion spaces will be discussed systematically with controllers, and the analysis conditions for synchronization to start and disappear will be given. Through numerical simulations, partial synchronization and full synchronization among three systems will be realized, which proves the validity of this method and is conducive to the further study of the synchronization of complex periodic and chaotic motions