An equivalent stochastic system model for control of chaotic dynamics

This paper investigates an equivalence relation between chaotic and stochastic systems, and presents an equivalent stochastic system model and a learning control strategy for control of chaotic dynamics. The equivalency in invariant measure and ergodicity between the two systems is defined. Based on the definition, the equivalence relation is studied and the equivalent stochastic system model of the chaotic system is derived analytically. The concept of the equivalency can be used to achieve system reconstruction using time series of chaotic systems and to develop the learning control strategy for control of chaotic dynamics