Global Analysis of an Asymmetric Continuous Piecewise Linear Differential System with Three Linear Zones

In [Chen et al., 2020], the third author and other coauthors studied global dynamics of the following system: [Formula: see text] in the parameter region [Formula: see text]. To study completely the piecewise linear system, we consider the parameter region [Formula: see text] in this paper. Firstly, we study the local dynamics, such as the bifurcations of equilibria (including the equilibrium at infinity). Secondly, the number and stability of limit cycles are studied completely. Then, we analyze the existence of upper and lower saddle connections and homoclinic loops. Moreover, we show that there are no heteroclinic loops in this parameter region. Finally, we give the bifurcation diagram and all global phase portraits on the Poincaré disc are given as well as some numerical examples.

Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear Systems

In this paper, we consider the realization of configuration of limit cycles of piecewise linear systems on the plane. We show that any configuration of finite number of Jordan curves can be realized by a discontinuous piecewise linear system with two zones separated by a continuous curve.