The boundary focus-saddle bifurcation in planar piecewise linear systems. application to the analysis of memristor oscillators
This paper deals with bifurcation analysis of piecewise linear planar systems with a straight line \(\Sigma\), say the \(y\)-axis, separating the plane \(\mathbb{R}^2\) into two regions, \(S_L\) and \(S_R\). It requires the system to be refracting, i.e. the first component equation is continuous on \(\mathbb{R}^2\). So there are two possible cases: the second component equation is continuous or discontinuous on \(\Sigma\). In each of the cases, the system can be reduced to a canonical form to ease the analysis, and it shows that a boundary focus-saddle equilibrium bifurcation leads to one stable limit cycle surrounding the unstable focus under some condition, a homoclinic connection under another condition, and neither limit cycles nor homoclinic connections otherwise. Although there exist some results on piecewise continuous dynamical systems in the literature, this paper focuses on bifurcation analysis and applications of such systems.
scientific article; zbMATH DE number 6892738
scientific article