Sliding bifurcations and non-determinism in systems with switching

Dynamical events associated with loss of determinacy in piecewise-smooth dynamical systems are reviewed. The causes of non-determinacy are discussed, and the conditions for their occurence in general systems are derived. These events can be characterized in terms of recently classified catastrophic sliding bifurcations and a non-deterministic form of chaos, which are shown to provide generic scenarios for non-determinacy to affect stable dynamical behaviour. The particular conditions for these are derived in a canonical (Lur'e) model of switched feedback control, and explicit examples are given in two and three dimensions.