In this paper, we extend the well-known Melnikov theory for smooth systems to a class of two-
zonal planar hybrid piecewise smooth systems. In this class, each zone of differentiability is …

We use the theory of differential inclusions, Filippov transformations and some appropriate
Poincaré maps to discuss the special case of two-dimensional discontinuous piecewise …

This book illustrates the correlation between connected citizens and smart communities and
cities. It delves into the fundamental element of smart communities, the concept of a unified …

Using first integrals we introduce an alternative tool to the Poincaré maps in order to study
the limit cycles of piecewise linear differential systems. It is also shown that an usual …

In this paper we present a relationship between the algebraic notion of proper system, the
geometric notion of contact point and the dynamic notion of Poincaré map for piecewise …

We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in
a class of piecewise linear differential systems, which appears in a natural way in control …

The class of piecewise-linear differential systems (PWL systems, for short) is an important
class of nonlinear dynamical systems from several points of view. First, they naturally appear …

Dynamical systems are relevant whenever one wants to describe evolution problems with
respect to time, usually given by ordinary or partial differential equations, or by the …

The class of piecewise-linear differential systems (PWL systems, for short) is an important
class of nonlinear dynamical systems. They naturally appear in realistic nonlinear …

A very useful approach to understand the complex behavior of a system is to consider its
degenerate situations. Accordingly the structure of periodic orbits for some degenerate …