Related papers: Symmetric Limit Cycles in 3D Piecewise Linear Syst…
We study limit cycles in piecewise complex systems with switching manifold $\mathbb{S}^1$. Using M\"obius transformations we establish an equivalence between circular and straight-line discontinuities that preserves periods, stability, and…
Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated…
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this…
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 ones as $\epsilon\rightarrow 0$. In slow-fast systems, the slow…
In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view: study of…
In recent decades, piecewise linear differential systems have attracted considerable attention due to their ability to describe a wide range of phenomena. A central problem, as in the theory of general planar differential systems, is to…
This paper presents new results on the limit cycles of a Li\'enard system with symmetry allowing for discontinuity. Our results generalize and improve the results in [33,34]. The results in [34] are only valid for the smooth system. We…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…
We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…
The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow…
In this article we study the existence of limit cycles in families of piecewise smooth differential equations having the unit circle as discontinuity region. We consider families presenting singularities of center or saddle type, visible or…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \begin{eqnarray*} (\dot{x},\ \dot{y})=\begin{cases} (-y(x+a)^2+\varepsilon…
In this paper, we study the existence of limit cycles in continuous and discontinuous planar piecewise linear Hamiltonian differential systems with two or three zones separated by straight lines and such that the linear systems that define…
We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincar\'e map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits…
In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of…
The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear $VI_3$ two-fold using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the…