Fast synchronization of directionally coupled chaotic systems

This paper studies the fast synchronization of directionally coupled chaotic systems under a chained interaction topology. Firstly, by applying finite-time stability theory, it is shown that all chaotic systems can achieve synchronization in finite time as long as the coupling strength is strong enough. Secondly, it is proved that the settling times are determined by the interaction strength, system parameters and initial conditions of the chaotic systems. Furthermore, it is found that the settling times are mainly dependent on the bounded value and dimension of the coupled chaotic systems when the individual chaotic sub-system is bounded. Finally, illustrative examples and numerical simulations are given to show the correctness of theoretical results.