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 study, a review is presented on previous work referring to analytical modeling of
mechanical systems having components that come in contact during their motion in ways …

The main objective of this work is to develop, via Brower degree theory and regularization
theory, a variation of the classical averaging method for detecting limit cycles of certain …

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 …

This work is dedicated to the memory of Donato Trigiante who has been the first teacher of
Numerical Analysis of the second author. The authors remember Donato as a generous …

If a set of ordinary differential equations is discontinuous along some threshold, solutions
can be found that are continuous, if sometimes multivalued. We show the extent to which …

In this paper, we provide a lower bound for the maximum number of limit cycles of planar
discontinuous piecewise linear differential systems defined in two half-planes separated by …

Sharp switches in behaviour, like impacts, stick–slip motion, or electrical relays, can be
modelled by differential equations with discontinuities. A discontinuity approximates fine …

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 …