Existence of periodic orbits and chaos in a class of three-dimensional piecewise linear systems with two virtual stable node-foci. (December 2021)

• Record Type: Journal Article
• Authors: Wei, Zhouchao; Zhu, Bin; Escalante-González, R.J.
• Is Part Of: Nonlinear analysis. Volume 43(2022)
• Publication Date: 2021-12
• Subjects: Chaos -- Poincaré map -- Piecewise linear systems -- Periodic orbit -- Virtual stable node-focus; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2021.101114
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we consider a new class of piecewise linear (PWL) systems with two virtual stable node-foci (the meaning of "virtual" is from Bernardo et al. (2008)) which exhibits periodic orbits and chaos. This fact that PWL systems have no unstable equilibria but has chaos will unavoidably make the exploration of this chaos more complicated. Particular values for bifurcation diagram are provided. Based on mathematical analysis and Poincaré map, periodic orbits of this kind of system without unstable equilibrium points are derived, the corresponding existence theorems are given, and the obtained results are applied to specific examples.