Global dynamics of a special class of planar sector-wise linear systems

In this article, we study the global dynamics of a special class of planar sector-wise linear differential systems with two subsystems being the same except for their equilibriums. Taking the position of one equilibrium as the bifurcation parameter, we provide a complete analysis about sliding cycle bifurcation and sliding homoclinic bifurcation. Moreover, we obtain the existence of all important separatrix orbits and their dependence on the bifurcation parameter, including sliding heteroclinic orbit, heteroclinic cycle, limit cycle, sliding homoclinic cycle and sliding cycle. For more information see https://ejde.math.txstate.edu/Volumes/2024/57/abstr.html