Limit cycles in planar continuous piecewise linear systems

作者：Chen, Hebai^*; Li, Denghui; Xie, Jianhua; Yue, Yuan

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 47: 438-454.

DOI：10.1016/j.cnsns.2016.12.006

• Piecewise linear system
• Bifurcation
• Limit cycle
• Periodic orbit

In this paper an asymmetric planar continuous piecewise linear differential system with three zones x = y - F(x), y = -g(x) is considered. The aim of this paper gives a completely study of limit cycles when this system satisfies such conditions and the uniqueness equilibrium does not lie in the central region. When (x - x(0))g(x) > 0 for for all x not approximate to x(0) and y = F(x) is a Z-shaped curve, it owns at most two limit cycles, which exist between a linear Hopf bifurcation surface and a double limit cycle bifurcation surface. Moreover, we prove the conjectures proposed by Ponce et al. [27]. When the uniqueness equilibrium lies in the central region, this system has exactly one limit cycles by others. Finally, some numerical examples are demonstrated.

• 出版日期2017-6
• 单位西南交通大学