Global fixed-time synchronization of chaotic systems with different dimensions

This paper studies the global fixed-time synchronization (GFTS) of chaotic systems with different dimensions. First, with the help of fixed-time stability theory of dynamic systems, a novel control protocol is put forward, which can achieve globally synchronization of two different dimensional chaotic systems (DDCS) in fixed time. Second, the GFTS of DDCS with uncertain parameters is also considered. The appropriate adaptive laws are designed to address the unknown parameters of the systems. Then, by the adaptive control, a new controller is presented to ensure the realization of DDCS within a given fixed time. Third, the GFTS is considered to networked DDCS, and the controller is also proposed accordingly. Different from conventional finite-time synchronization, the upper bound of settling time is independent of initial conditions of systems in GFTS. Finally, the effectiveness of the obtained results is demonstrated by corresponding numerical simulations.