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 …

For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …

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 …

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 …

Non-smooth systems can generate dynamics and bifurcations that are drastically different
from their smooth counterparts. In this paper, we study such homoclinic bifurcations in a …

We recall three well-known theorems related to the simplest codimension-one bifurcations
occurring in discrete time dynamical systems, such as the fold, flip and Neimark–Sacker …

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives
the dynamics of a stock market model. This model is a modification of our previous model …

Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear
map) can persist throughout open regions of parameter space. Such robust chaos has been …

Corporate demand for cash is related to a number of firm-specific characteristics, like the
presence of transaction costs, information asymmetry in credit markets, uncertainty and risk …

This survey article is concerned with the study of bifurcations of discontinuous piecewise-
smooth maps, with a special focus on the one-dimensional case. We review the literature on …