Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type. (August 2019)

• Record Type: Journal Article
• Authors: Wang, Jiafu; Huang, Chuangxia; Huang, Lihong
• Is Part Of: Nonlinear analysis. Volume 33(2019)
• Page Start: 162
• Page End: 178
• Publication Date: 2019-08
• Subjects: Planar piecewise linear system -- Limit cycle -- Liénard-like canonical form -- Stability -- Discontinuity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.03.004
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: The aim of this paper is to deal with the problem of limit cycles for a general planar piecewise linear differential system of saddle–focus type. By using the Liénard-like canonical form with five parameters and dividing the total parameter space into several regions, the number of limit cycles is discussed in detail. In particular, we give parameter regions where there are at least two limit cycles. Moreover, we investigate the existence and stability of exactly two nested limit cycles in some parameter regions. Highlights: Limit cycles are induced by discontinuity of the system being saddle–focus type. The number of limit cycles is discussed in detail by dividing the total parameter space into several regions. Some parameter regions are given where there are exactly two limit cycles or a unique one. A new distance function is applied to discuss the number of limit cycles. The sufficient conditions on the existence of limit cycles can be directly verified according to the parameters of the system.