Establishing definitive conditions for monodromic equilibria and centers of continuous piecewise linear systems with arbitrary finite number of switching lines

Abstract

This paper aims to provide sufficient and necessary conditions for the monodromic problem and center problem of continuous piecewise linear systems with arbitrary finite number of switching lines. Notice that a system under arbitrary small perturbation with the continuous piecewise linear class has the same number of switching lines, implying that the monodromic equilibrium is structurally unstable. Then, we give the versal unfoldings of the monodromic equilibrium of the continuous piecewise linear system with a switching line and bifurcation diagrams and all phase portraits of these versal unfoldings.