On double boundary equilibrium bifurcations in piecewise smooth planar systems (Q1936519)

Non-smooth dynamical systems arise in a natural way in several branches of physics, for instance when modeling a variety of mechanical or electronic devices. An important family of non-smooth dynamical systems are the planar piecewise linear systems. In this context, the authors study the occurrence of boundary equilibria bifurcations (BEBs), that is, collisions of an equilibrium point with the discontinuity boundary. After a brief review on Filippov systems, Section 3 gives an improved proof of the characterization theorem for BEBs. Then, Section 4 is devoted to the analysis of the bifurcation set for a particular system, illustrating the complexity that may appear even in simple examples. The authors argue that the case under consideration seems to be a section of a higher-codimension bifurcation point.