Existence of Limit Cycles for a Cubic Kolmogorov System with a Hyperbolic Solution

When we discuss some problems in bio-mathematics,we often meet cubicKolmogorov systems.For general type of Kolmogorov systems,the qualitative analysisis very difficult. Usually,one discusses some special type of cubic Kolmogorovsystems,for example,cubic Kolmogorov systems with an algebraic curve solution.Firstly,the existence oflimitcycles fora cubic Kolmogorov system with quadratic curvesolution was studied.In article[1 ] ,though the author proved the cubic Kolmogorovsystem with a solution…     

金融危机传染的非线性动力学模型

越来越多的证据表明全球金融市场是高度复杂,广泛联接的非线性动力系统网络,由于系统的非线性和复杂性特征使得金融危机极易通过系统间的耦合作用而发生传染.针对金融危机传染所表现出的非线性动力学特性,本文构建了以传染源国家和受传染国家股票收益率为变量的微分动力学传染模型.利用微分方程定性理论对模型的奇点进行讨论,得出极限环存在的条件及形式,并进而得出金融危机传染的三种情况:轻度传染、可控传染和强烈传染.     

Schrijver图SG(2k+2,k)的Hamilton性

通过图G的每个顶点的路称为Hamilton路,通过图G的每个顶点的圈称为Hamilton圈,具有Hamilton圈的图G称为Hamilton图.1952年Dirac曾得到关于Hamilton图一个充分条件的结论:图G有n个顶点,如果每个顶点υ满足:d(υ)≥n/2,则图G是Hamilton图.本文研究了Schrijver图SG(2k+2,k)的Hamilton性,采用寻找Hamilton圈的方法得出了Schrijver图SG(2k+2,k)是Hamilton图.     

关于一类非多项式平面微分系统的极限环及分支问题

旨在讨论一类非多项式平面微分系统.通过使用Dulac准则和Bendixson准则获得极限环不存在性的充分条件,引入广义Liénard系统理论以研究极限环的存在性及稳定性,应用Hopf分岔理论证明自原点分岔出极限环的充分条件.此外,给出一个范例以验证分析和结果的有效性.     

Closure and stable Hamiltonian properties in claw‐free graphs

In the class of k‐connected claw‐free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an infinite family of graphs G_k of arbitrarily high connectivity k such that the closure of G_k has the property while the graph G_k does not); (ii) traceability is a stable property even for k = 1; (iii) homogeneous traceability is not stable for k = 2 (although it is stable for k = 7). The article is concluded with several open questions concerning stability of homogeneous traceability and Hamiltonian connectedness. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 30–41, 2000     

Half‐transitive graphs of valency 4 with prescribed attachment numbers

A graph X is said to be ½‐transitive if its automorphism group Aut X acts vertex‐ and edge‐, but not arc‐transitively on X. Then Aut X induces an orientation of the edges of X. If X has valency 4, then this orientation gives rise to so‐called alternating cycles, that is even length cycles in X whose every other vertex is the head and every other vertex is the tail of its two incident edges in the above orientation. All alternating cycles have the same length 2r(X), where r(X) is the radius of X, and any two adjacent alternating cycles intersect in the same number of vertices, called the attachment number a(X) of X. All known examples of ½‐transitive graphs have attachment number 1, r or 2r, where r is the radius of the graph. In this article, we construct ½‐transitive graphs with all other possible attachment numbers. The case of attachment number 2 is dealt with in more detail. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 89–99, 2000     

Self‐converse Mendelsohn designs with block size 4 and 5

A (v, k, λ)‐Mendelsohn design(X, ℬ︁) is called self‐converse if there is an isomorphic mapping ƒ from (X, ℬ︁) to (X, ℬ︁⁻¹), where ℬ︁⁻¹ = {B⁻¹ = 〈x_k, x_k−1,…,x₂, x₁〉: B = 〈x₁, x₂,…,x_k−1, x_k〉 ϵ ℬ︁}. In this paper, we give the existence spectrum for self‐converse (v, 4, 1)– and (v, 5, 1)– Mendelsohn designs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 411–418, 2000     

有向圈的行列式算法及HAMILTON图条件

本文引入有向路乘法、弧行列式等概念 ,讨论了弧行列式的性质 ,阐述了二种计算有向圈的行列式方法及有向图 D为 Hamilton图的充要条件 ,最后给出了计算实例     

一类Holling功能性反应模型极限环的唯一性

考虑捕食者无密度制约，食饵具有非线性密度制约的第三类Ｈｏｌｌｉｎｇ功能性反应捕食者－食饵系统．对该系统给出了完整的定性分析，证明了该系统至多有一个极限环，存在极限环的充要条件是正平衡点不稳定．     

Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles

Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after iterations of various shuffling methods. We emphasize the role of Cauchy type identities and variations of the Robinson-Schensted-Knuth correspondence.