Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach.
First, a type of Q-S (complete or anticipated) synchronization is defined in discrete-time dynamical systems. Second, based on backstepping design with a scalar controller, a systematic, concrete and automatic scheme is presented to investigate Q-S (complete or anticipated) synchronization between the discrete-time drive system and response system with strict-feedback form. Finally, the proposed scheme is used to illustrate Q-S (complete or anticipated) synchronization between the two-dimensional discrete-time Lorenz system and Fold system, as well as the three-dimensional hyperchaotic discrete-time Rossler system and generalized discrete-time Rossler system. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. Our scheme can be also extended to investigate Q-S (complete or anticipated) synchronization between other discrete-time dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller and to verify its effectiveness in computer.
Yan
Zhenya
Z
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100080, People's Republic of China. zyyan@mmrc.iss.ac.cn