Our study is concerned with a particular class of hybrid dynamical systems, namely systems with discontinuous vector fields. We will show that such systems can exhibit a novel class of bifurcations which are not observed in smooth dynamical systems. Particularly, we concentrate on bifurcations which arise due to the existence of so-called sliding motion. Using appropriate discrete mappings we show the possible existence of complex transitions which we term sliding, multisliding and grazing-sliding bifurcations. Relay feedback systems are used as a representative example.
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