Chaotic attractor generation and critical value analysis via switching approach

The generation of novel chaotic funnel-shaped attractors is introduced and the analysis of related critical values is given with a proposed switching method in this paper. The underlying mechanism involves a simple three-dimensional switched system and a hysteretically switching signal. Moreover, theoretic analysis is carried out to study the attractor generation and the corresponding critical values by fully utilizing the specific structure of the non-smooth system. Based on carefully derivation, the critical values and related stability regions of the created attractors are estimated explicitly, which is usually impossible for general non-smooth dynamics. In addition, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable system parameters.