A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems

This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium bifurcations of hybrid systems, Filippov systems, and continuous systems, and limit cycles created from folds and by the addition of hysteresis or time-delay. In each case a stationary solution, such as a regular equilibrium, changes stability and possibly form and emits one limit cycle. Scaling laws for the amplitude and period of the limit cycles are compared to (classical) Hopf bifurcations.