Global dynamics of an asymmetry piecewise linear differential system: Theory and applications

摘要

In this paper, we have completely studied a four-parameter family of continuous piecewise linear differential systems with three linear regions and no symmetry in the compactification space of R-2. The bifurcation diagram and the corresponding global phase portraits of the continuous piecewise linear system are derived. It is shown that the continuous piecewise linear system has rich dynamics such as three isolated equilibria, three limit cycles, a figure-eight loop and a homoclinic loop which likes a cuspidal loop in R-2 for some parameters values, respectively. As applications of our results, we can obtain the global dynamics of continuous piecewise linear FitzHugh-Nagumo equation and non-symmetric memristor-based electronic oscillators, respectively. (C) 2020 Elsevier Masson SAS. All rights reserved.