Related papers: Limit cycles in refracted Hamiltonian systems with…

This paper contains two parts. In the first part, we shall study the Abelian integrals for Zoladek's example [13], in which it is claimed the existence integrals of 11 small-amplitude limit cycles around a singular point in a particular…

For linear control systems with bounded control range, chain controllability properties are analyzed. It is shown that there exists a unique chain control set and that it equals the sum of the control set around the origin and the center…

This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. By analyzing the obtained first order Melnikov function, we give an upper bound of the number of limit cycles…

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 present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method…

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…

Continuing the investigation for the number of crossing limit cycles of nonsmooth Li\'enard systems in [Nonlinearity 21(2008), 2121-2142] for the case of a unique equilibrium, in this paper we consider the case of any number of equilibria.…

We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it is shown that the input size of the converted instance is a…

Renormalization group limit cycles may be a commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience to date with classical models of critical points, where fixed points are far more common. We discuss the…

In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.

The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using the notion of slow divergence integral and elementary…

We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic…

In the study of the number of limit cycles of near-Hamiltonian systems, the first order Melnikov function plays an important role. This paper aims to establish a development of a known method to estimate the upper bound of the number of…

This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincar\'e--Bendixson regions by using transversal curves, that enables us to…

It this paper we study a class of perturbed Hamiltonian systems under perturbations of thirteen order in order to detect the number of limit cycles which bifurcate from some periodic orbits of the unperturbed Hamiltonian system. The system…

In this paper, we study the bifurcate of limit cycles for Bogdanov-Takens system($\dot{x}=y$, $\dot{y}=-x+x^{2}$) under perturbations of piecewise smooth polynomials of degree $2$ and $n$ respectively. We bound the number of zeros of first…

We introduce a class of linear compartmental models called identifiable path/cycle models which have the property that all of the monomial functions of parameters associated to the directed cycles and paths from input compartments to output…

In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide…

We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…

Let $(x(t),y(t))^\top$ be a solution of a Fuchsian system of order two with three singular points. The vector space of functions of the form $P(t)x(t)+Q(t)y(t)$, where $P,Q$ are real polynomials, has a natural filtration of vector spaces,…