Bifurcations of equilibria in non-smooth continuous systems

The aim of this paper is to show a variety of bifurcation phenomena of equilibria that can be observed in non-smooth continuous systems. In non-smooth systems so-called ‘multiple crossing bifurcations’ can occur, for which the eigenvalues jump more than once over the imaginary axis, and which do not have a classical bifurcation as counterpart. Novel theoretical results are given for a class of planar systems but no general theory is available for the multi-dimensional case. A number of well chosen examples of multiple crossing bifurcations are discussed in detail.