In this dissertation, we present results on the existence of limit cycles in planar differential systems, configuration of such cycles and the dynamics of nonlinear systems near periodic orbits.

We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincare map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that ...

The Lienard equation x + f (x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions ...

The aim of this article is twofold. Firstly, we study the existence of limit cycles in a family of piecewise smooth vector fields corresponding to an unfolding of an invisible fold–fold singularity. More precisely, given ...

Estudamos dois critérios sobre a não existência ou existência e unicidade de ciclos limites para campos vetoriais planares. Aplicamos esses critérios em algumas famílias de campos vetoriais quadráticos e cúbicos, além de ...

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit ...

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit ...

In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the ...

In this work, a modified Rosenzweig-MacArthur predator-prey model is analyzed, which is a particular Gause type model, considering two Allee effect affecting the prey population. This phenomenon may be expressed by different ...