Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation is developed.