Shooting for border collision bifurcations in hybrid systems

Border collision bifurcations refer to situations where a small parameter variation induces a change in the event sequence of a hybrid system. At such a bifurcation, the system trajectory makes tangential contact with an event triggering hypersurface. This bounding case separates regions of (generally) quite different dynamic behaviour. In the paper, the conditions governing bifurcation points are formulated as a boundary value problem. A shooting method is used to solve that problem. The approach is applicable for general nonlinear hybrid systems.