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 we develop an arbitrary order Melnikov function to study limit cycles bifurcating
from a periodic submanifold for autonomous piecewise smooth differential systems in R n …

In a smooth dynamical system, a homoclinic connection is an orbit connecting a saddle
equilibrium to itself. Under perturbation, homoclinics are associated with bifurcations of …

The averaging theory for studying periodic orbits of smooth differential systems has a long
history. Whereas the averaging theory for piecewise smooth differential systems appeared …

Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise
linear vector fields on the plane when the switching curve is xy= 0. We consider the …

This paper deals with the maximum number of limit cycles, which can be bifurcated from
periodic orbits of planar piecewise smooth Hamiltonian systems, which are located in a …

For planar systems with a pseudo-equilibrium point of focus type within its discontinuity line,
computable normal forms are introduced. Thus, the classical theory of normal forms is …

In this paper, we show the existence of piecewise linear differential system with two zones in
the plane having the following features: it has a center and a saddle singularity point in each …

We consider an n dimensional dynamical system with discontinuous right-hand side
(DRHS), whereby the vector field changes discontinuously across a co-dimension 1 …

In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a
scenario, the main goal of this paper is to exhibit the homeomorphism that gives the …