PERIODIC SOLUTIONS FOR A CLASS OF DEGENERATE NEUTRAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point method, discusses the problem of periodic solution for a class of degenerate neutral periodic system with delay, and obtains some sufficient conditions for the existence and uniqueness of periodic solution of the system, the result extends and improves some results of paper [1-2].     

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

SOURCE－TYPE SOLUTIONS OF A QUASILINEAR DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

ＳＯＵＲＣＥ－ＴＹＰＥ ＳＯＬＵＴＩＯＮＳ ＯＦ Ａ ＱＵＡＳＩＬＩＮＥＡＲ ＤＥＧＥＮＥＲＡＴＥ ＰＡＲＡＢＯＬＩＣ ＥＱＵＡＴＩＯＮ ＷＩＴＨ ＡＢＳＯＲＰＴＩＯＮ￥ＺＨＡＯＪＵＮＮＩＮＧＡｂｓｔｒａｃｔ：Ｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｎｏｎｅｘ...     

DYNAMICS FOR VORTICES OF AN EVOLUTIONARY GINZBURG－LANDAU EQUATIONS IN 3 DIMENSIONS

91. Introduction\Nb consider thc fOllowing problemwhere Q = fl x I0, l], fl C R2 is a bounded smooth domaill, g f Z = afl x I0, l] - Sl is aC"-map such that deg(g,0O.) = d > 0 fOr all 0 5 = 5 l. Herc fl. = n x {z}. fi f Q --+ Ris a smooth function (sa}' C'(Q)) with positivc lowcr bound. ue t Q x R+ - R2.The aim of this article is to understand thc dynamics of vortices, or zeros, of solutionsu of (l.1)--(l.4). lts importance to the theory of superconductivity and applications areaddress…     

LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS

In this paper,we are concerned with a cubic near-Hamiltonian system,whose unperturbed system is quadratic and has a symmetric homoclinic loop.By using the method developed in [12],we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop.Further,we give a condition under which there exist 4 limit cycles.     

Quadratic perturbations of quadratic codimension-four centers

We study the stratum in the set of all quadratic differential systems , with a center, known as the codimension-four case Q₄. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincaré-Pontryagin-Melnikov integral I. We show that the orbits of the unperturbed system are elliptic curves, and I is a complete elliptic integral. Then using Picard-Fuchs equations and the Petrov's method (based on the argument principle), we set an upper bound of eight for the number of limit cycles produced from the period annulus around the center.     

Limit Cycles Bifurcating from a Quadratic Reversible Lotka-Volterra System with a Center and Three Saddles

This paper is concerned with limit cycles which bifurcate from a period annulus of a quadratic reversible Lotka-Volterra system with sextic orbits. The authors apply the property of an extended complete Chebyshev system and prove that the cyclicity of the period annulus under quadratic perturbations is equal to two.     

MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR HAMILTONIAN SYSTEM

In this paper, Melnikov functions which apper in the study of limit cycles of a perturbed planar Hamiltonlan system are studied. There are two main contributions here. The first one is related to the explicit formulae for these functions: a new method is developed to achieve the goal for the second one (Theorem A). the authors also discover a close relation between Melnlkov functions and focal qtmntities (Theorem 13). This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function (see §5). I)espite these results, this paper also includes other related resuEs, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system.     

SAME DISTRIBUTION OF LIMIT CYCLES TO PERTURBED CUBIC HAMILTONIAN SYSTEMS WITH DIFFERENT PERTURBATIONS

Using qualitative analysis, we study perturbed Hamiltonian systems with different n-th order polynomial as perturbation terms. By numerical simulation, we show that these perturbed systems have the same distribution of limit cycles. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.     

THE QUADRATIC SYSTEM WITH NONHYPERBOLIC HOMOCLINIC CYCLE

In this paper, we will show some sufficient conditions to assert certain system existing nonhyperbolic homoclinic cycles.     

再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．     

具有二个焦点的二次系统

本文证明了具有二个焦点的二次系统,若其无穷远奇点多于一个,则必在其中一个焦点外围至多有一个极限环,再由作者以前的文章得到：二次系统之极限环不可能出现（２ｉ,２ｊ）分布（ｉ,ｊ＝１,２,……）。     

具有无限时滞的退化微分系统的周期解

考虑具有无限时滞的中立型退化微分系统E(t)d/dt[x(t) -∫t-∞C(t,s)x(s)ds]=A(t)x(t)+f(t,x(t-τ(t))+b(t)的周期解的存在性和唯一性问题,利用线性系统指数型二分性理论和Krasnoselsku不动点定理研究此系统,并通过技巧性代换获得了保证其周期解存在性和唯一性的充分性条件,得到了一些新的结果,推广了相关文献的主要结果.