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 …

In this article some qualitative and geometric aspects of non-smooth dynamical systems
theory are discussed. The main aim of this article is to develop a systematic method for …

This paper presents an overview of the current state of the art in the analysis of discontinuity-
induced bifurcations (DIBs) of piecewise smooth dynamical systems, a particularly relevant …

In this paper, a local theory of non-smooth dynamical systems on connectable and
accessible sub-domains is developed. The properties for separation boundaries based on …

Discontinuities are encountered when objects collide, when decisions are made, when
switches are turned on or off, when light and sound refract as they pass between different …

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The
focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting …

Non-smooth dynamical system Systems derived from ordinary differential equations when
the non-uniqueness of solutions is allowed. In this article we deal with discontinuous vector …

When a vector field in R^3 is discontinuous on a smooth codimension one surface, it may be
simultaneously tangent to both sides of the surface at generic isolated points (singularities) …

This paper is concerned with some aspects of the qualitative–geometric theory of non-
smooth systems. We present a survey of the state of the art on the connection between the …

Using the singularity theory of scalar functions, we derive a classification of sliding
bifurcations in piecewise-smooth flows. These are global bifurcations which occur when …