Precise planement of all Lyapunov exponents for discrete-time dynamical systems

Abstract

In this paper, a new algorithm for all Lyapunov Exponents precisely configuraling a discrete-time dynamical system is proposed. A given deterministic discrete-time dynamical system can be chaotified by the algorithm. A new feed-back controller is designed via moduling operation. All Lyapunov Exponents of the controlled system are equal to a given set of ones. The new controller is simple and can be used to control or anti-control a chaotic system . The corresponding proof as well as two illustrative examples are presented. The simulation results show the effectiveness of the algorithm.