Generating chaos via decentralized linear state feedback and a class of nonlinear functions

This paper proposes a general chaotification algorithm for a class of nonlinear discrete-time dynamical systems. Based on a given nonlinear discrete-time system, the new chaotification algorithm uses the decentralized linear state feedback control and a class of nonlinear functions that are only required to satisfy some mild assumptions to construct a chaotic nonlinear system. The sine and sawtooth function used in the existing literature on chaotification only are the special cases of the proposed nonlinear function. Based on the corrected version of the Marotto theorem, we mathematically prove that the constructed nonlinear system is indeed chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is also obtained. The theoretical results in this paper can be used to supervise one to construct different chaotification algorithms.