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 …

1. Fundamentals of piecewise-smooth, continuous systems. 1.1. Applications. 1.2. A
framework for local behavior. 1.3. Existence of equilibria and fixed points. 1.4. The observer …

Much progress has been made in planar piecewise smooth dynamical systems. However
there remain many important problems to be solved even in planar piecewise linear …

For many physical systems the transition from a stationary solution to sustained small
amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts …

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 …

The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model.
The time delay in the tyre–ground contact and the non-smooth nature of the system caused …

The creation or destruction of a crossing limit cycle when a sliding segment changes its
stability, is known as pseudo-Hopf bifurcation. In this paper, under generic conditions, we …

Large scale studies of spiking neural networks are a key part of modern approaches to
understanding the dynamics of biological neural tissue. One approach in computational …

In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of
switching systems in R 3 are studied. In particular, a dc–dc boost converter with sliding …

This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-
dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium …