Open AccessCoexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems
Author(s) -
Kai Li,
Wenjing Xu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022045
Subject(s) - homoclinic orbit , heteroclinic cycle , chaotic , heteroclinic bifurcation , heteroclinic orbit , mathematics , invariant (physics) , affine transformation , class (philosophy) , piecewise , mathematical analysis , pure mathematics , computer science , nonlinear system , bifurcation , physics , mathematical physics , quantum mechanics , artificial intelligence , period doubling bifurcation
Detecting an isolated homoclinic or heteroclinic cycle is a great challenge in a concrete system, letting alone the case of coexisting scenarios and more complicated chaotic behaviors. This paper systematically investigates the dynamics for a class of three-dimensional (3D) three-zone piecewise affine systems (PWASs) consisting of three sub-systems. Interestingly, under different conditions the considered system can display three types of coexisting singular cycles including: homoclinic and homoclinic cycles, heteroclinic and heteroclinic cycles, homoclinic and heteroclinic cycles. Furthermore, it establishes sufficient conditions for the presence of chaotic invariant sets emerged from such coexisting cycles. Finally, three numerical examples are provided to verify the proposed theoretical results.