A Lie-based approach to the general framework of chaotic synchronization

Abstract

"Diverese phenomena have been reported on the synchornization of chaotic systems. Therefore, the generalized framework of the chaotic synchronization is an actual scienti¯c debate. Here, a Lie-based geometrical approach is presented to remark some geometrical properties of the nonlinear (chaotic) systems toward their synchronization. That is, we address the general problem of ¯nding the conditions for the existence of the synchronization function y = ¸(x). The contribution is focused on the 2 and 3 dimensional (unidirectionally coupled) systems. Illustrative examples are provided along the text."