Three Forms of Dynamical Chaos

Abstract

This work is a review of recent results, which have been obtained within the framework of the mathematical theory of dynamical chaos and are related to the discovery of its third new form, the so-called mixed dynamics. This type of chaos considerably differs from its two classical forms, namely, conservative chaos and dissipative chaos, and the main difference is that attractors and repellers can intersect without coincidence. This work offers theoretical substantiation of this phenomenon without involving a serious mathematical apparatus and also provides a number of examples of the systems from applications in which the mixed dynamics is observed. We show that the mixed dynamics can be of different types, ranging from that close to conservative to the strongly dissipative one, and that it can result from various bifurcation mechanisms.