In this paper we deal with nonlinear differential systems of the form where $ F_i:\mathbb
{R}\times D\rightarrow\mathbb {R}^ n $ for i= 0, 1,..., k, and $ R:\mathbb {R}\times D\times …

Some techniques for proving the existence and uniqueness of limit cycles for smooth
differential systems are extended to continuous piecewise linear differential systems with …

In this paper, we consider the first-order Melnikov functions and limit cycle bifurcations of a
near-Hamiltonian system near a cuspidal loop. By establishing relations between the …

This paper provides the classification of the phase portraits in the Poincaré disc of all
piecewise linear continuous differential systems with two zones separated by a straight line …

This work is devoted to study the existence of periodic solutions for a class of ε-family of
discontinuous differential systems with many zones. We show that the averaged functions at …

By means of the averaging method of the first order, we introduce the maximum number of
limit cycles which can be bifurcated from the periodic orbits of a Hamiltonian system …

In this paper, we make a complete study on small perturbations of Hamiltonian vector field
with a hyper-elliptic Hamiltonian of degree five, which is a Liénard system of the form x′= y …

Liénard systems are very important mathematical models describing oscillatory processes
arising in applied sciences. In this paper, we study polynomial Liénard systems of arbitrary …

In this paper, we extend the slow divergence-integral from slow-fast systems, due to De
Maesschalck, Dumortier and Roussarie, to smooth systems that limit onto piecewise smooth …

We study the number of limit cycles which can bifurcate from the periodic orbits of a linear
center perturbed by nonlinear functions inside the class of all classical polynomial Liénard …