The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems. (February 2018)

• Record Type: Journal Article
• Authors: Wang, Lei; Yang, Xiao-Song
• Is Part Of: Nonlinear analysis. Volume 27(2018)
• Page Start: 157
• Page End: 173
• Publication Date: 2018-02
• Subjects: Periodic orbits -- Sink -- Saddle -- Poincaré map -- Fixed points -- Piecewise affine systems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.08.010
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper investigates the existence and stability of periodic orbits in a class of 3-dimensional piecewise affine systems with two zones. Two results on the existence of periodic orbits are obtained by applying some fixed points theorems to a Poincaré map. Precisely, we prove the existence of a periodic sink in one case and a periodic saddle in another case. Finally, some concrete examples are given to illustrate the main results.