Research On Function Projective Synchronization Of Discrete Chaotic Systems

Function projective synchronization of chaotic systems is one of the important research fields, but most of the relevant researches only focused on continuous chaotic systems with same order. In this paper several methods are presented to investigate function projective synchronization of discrete chaotic systems.Firstly, a new controller is designed to realize the hybrid function projective syn-chronization of discrete chaotic systems in feedback synchronization theory. Secondly, because synchronization of different orders and time-delay exists widely in many practi-cal applications and the related research is few, another approach is proposed to achieve the hybrid lag function projective synchronization of discrete chaotic systems with dif-ferent orders by variable-iteration way, which is discussed under the conditions of in-creased order and decreased order, respectively. Compared with the commonly used lag synchronization, the feature of this paper is that not only do the variables exist time-delay, but also the functions exist it, which is a beneficial supplement to lag syn-chronization. Besides, based on the Lyapunov stability theory, an appropriate Lyapunov function is created to demonstrate the validity of this new method.Finally, many numerical simulations are given to verify the effectiveness of the corresponding results.