Related papers: Limit cycles in refracted Hamiltonian systems with…
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…
Piecewise linear differential systems separated by two parallel straight lines of the type of center-center-Hamiltonian saddle and the center-Hamiltonian saddle-Hamiltonian saddle can have at most one limit cycle and there are systems in…
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…
In this paper we study the maximum number $N$ of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies…
We present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be…
This paper establishes a new Chebyshev criterion for some family of integrals. By virtue of this criterion we obtain several new Chebyshev families. With the help of these new families we can answer the conjecture posed by Gasull et al in…
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 are concerned about smoothing of Filippov systems around homoclinic-like connections to regular-tangential singularities. We provide conditions to guarantee the existence of limit cycles bifurcating from such connections.…
The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging…
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…
In this paper, we generalize the Picard-Fuchs equation method to study the bifurcation of limit cycles of perturbed differential systems with two switching lines. We obtain the detailed expression of the corresponding first order Melnikov…
In this paper, we study the number of limit cycles that can bifurcating from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove…
The already proved Lum-Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel…
In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus of discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the…
In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector…
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…
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…
In this paper a generalized Rayleigh-Li\'enard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the…
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…
In this paper we prove a sufficient condition for the existence of a Hamilton cycle, which is applicable to a wide variety of graphs, including relatively sparse graphs. In contrast to previous criteria, ours is based on only two…