A proof of Euzebio-Pazim-Ponce's conjectures for a degenerate planar piecewise linear differential system with three zones

被引:6
作者
Chen, Hebai [1 ]
Tang, Yilei [2 ]
机构
[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
[2] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China
基金
中国国家自然科学基金;
关键词
Lienard system; Piecewise linear system; Limit cycle; Bifurcation; Rotation; LIMIT-CYCLES; BIFURCATION SETS; UNIQUENESS;
D O I
10.1016/j.physd.2019.132150
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we study bifurcations and dynamics in a planar piecewise linear differential system with three zones (x)over dot = F(x) - y, (y)over dot = g(x) alpha. When the system is degenerate in the central zone, i.e., g'(x) = 0 in the central zone, and F(x) is a flute linear function, Euzebio, Pazim and Ponce in Euzebio et al. (2016) proposed three conjectures on limit cycles. The aim of this paper is to prove Euzebio-Pazim-Ponce's conjectures so that the number and the bifurcation of limit cycles of the degegerate planar piecewise linear differential system with three zones, i.e., under the same assumptions as in Euzebio et al. (2016), are studied completely. Finally, the bifurcation diagrams and the phase portraits of this planar piecewise linear differential system are given completely, including scabbard bifurcation, grazing bifurcation and double limit cycle bifurcation. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页数:22
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