Dynamics and bifurcations of nonsmooth systems: A survey

In this survey we discuss current directions of research in the dynamics of nonsmooth systems, with emphasis on bifurcation theory. An introduction to the state-of-the-art (also for non-specialists) is complemented by a presentation of the main open problems. We illustrate the theory by means of elementary examples. The main focus is on piecewise smooth systems, which have recently attracted a lot of attention, but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities. This extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context. A dedicated section is devoted to concrete applications that stimulate the development of the field. This survey is concluded by an extensive bibliography.