相关论文: The number of medium amplitude limit cycles of som…

We study the bifurcation of limit cycles from the periodic orbits of $2n$--dimensional linear centers $\dot{x} = A_0 x$ when they are perturbed inside classes of continuous and discontinuous piecewise linear differential systems of control…

This paper deals with the problem of limit cycle bifurcations for a piecewise near-Hamilton system with four regions separated by algebraic curves $y=\pm x^2$. By analyzing the obtained first order Melnikov function, we give an upper bound…

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…

This paper applies a recent result determining periodic orbits on the basis of first integrals, for Li\'enard systems. By solving a first order ODE with singularities, a crucial result is proved to locate intervals of single and isolated…

We find an upper bound to the maximal number of limit cycles, which bifurcate from a hamiltonian two-saddle loop of an analytic vector field, under an analytic deformation.

By using the Picard-Fuchs equation and the property of Chebyshev space to the discontinuous differential system, we obtain an upper bound of the number of limit cycles for the nongeneric quadratic reversible system when it is perturbed…

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…

We present a simpler proof of the existence of an exact number of one or more limit cycles to the Lienard system $\dot{x}=y-F(x) $, $\dot {y}=-g(xt)$, under weaker conditions on the odd functions $F(x) $ and $g(x) $ as compared to those…

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…

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach…

We consider the multiplicity of limit cycles that appear when a hyperbolic polycycle is perturbed. We prove, in particular, that if such unfolding happens in generic finite-parameter families, the multiplicity of every new limit cycle does…

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…

The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been subject of interest of hundreds of papers. After more than 30…

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This…

Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this…

In this paper, we perturb the global center of the planar polynomial vector fields $\mathcal{X}(x,y)=(-y(x^2+a^2),x(x^2+a^2))$ ($a\neq0$) inside cubic piecewise smooth polynomials with switching line $y=0$. By using average function of…

The aim of this paper is to investigate two classical problems related to nilpotent center conditions and bifurcation of limit cycles in switching polynomial systems. Due to the difficulty in calculating the Lyapunov constants of switching…

We obtain condition for existence of a center for a cubic planar differential system, which can be considered as a polynomial subfamily of the generalized Riccati system. We also investigate bifurcations of small limit cycles from the…

We consider perturbed pendulum-like equations on the cylinder of the form $ \ddot x+\sin(x)= \varepsilon \sum_{s=0}^{m}{Q_{n,s} (x)\, \dot x^{s}}$ where $Q_{n,s}$ are trigonometric polynomials of degree $n$, and study the number of limit…

The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$, $\dot{z}=0$, with $x,y \in R$ and $z\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles…