一个非线性时滞偏微分方程种群模型的稳定性与周期性

讨论了一个具有年龄结构非线性非自治时滞偏微分方程种群模型解的渐近性态,得到了零解稳定以及周期解存在的充分条件.     

Positive Periodic Solution for a Nonautonomous Delay Differential Equation

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.     

一类高维时滞微分方程的周期解

本文考虑高维时滞微分方程ｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－ｒ（ｔ）））其中（ｔ,ｘ）∈Ｒ^ｎ,Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵,ｆ（ｔ,ｘ）是ｎ维连续向量,ｒ（ｔ）是时间依赖的滞量,应用不动点定理,在确定的条件下,证明了该系统的周期解的存在性与唯一性     

带分布时滞中立型微分方程正解的存在性

主要运用Banach压缩映像原理,研究了分布时滞中立型微分方程ddty(t)+∫abP(t,θ)y(t-θ)dθ+∫cdQ(t,θ)y(t-θ)dθ=0正解的存在性问题,获得了正解存在的充分条件,推广了相关文献的结果.     

A Newton-Picard Collocation Method for Periodic Solutions of Delay Differential Equations

This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We exploit the equivalence of the linearized collocation system and the discretization of the linearized periodic boundary value problem (BVP). This linear BVP is solved using a variant of the Newton-Picard method [Int. J. Bifurcation Chaos, 7 (1997), pp. 2547–2560]. This method combines a direct method in the low-dimensional subspace of the weakly stable and unstable modes with an iterative solver in the high-dimensional orthogonal complement. As a side effect, we also obtain good estimates for the dominant Floquet multipliers. We have implemented the method in the DDE-BIFTOOL environment to test our algorithm. AMS subject classification (2000) 65J15, 65P30, 65Q05     

一类自变量分段连续的非线性延迟微分方程数值解振动性

主要考虑一类自变量分段连续的非线性延迟微分方程数值解的振动性.主要通过线性化的理论将非线性方程的振动性转化为线性方程的振动性,从而得到数值解振动的条件,进而得到线性θ-方法保持方程振动性的条件.为了更有力的说明我们的结果,最后给出了相应的算例.     

一类时滞脉冲微分方程的概周期解的存在性

运用锥上的不动点定理，研究一类脉冲时滞微分方程的概周期解，得到了保证系统存在概周期解的一组充分条件。     

Stability and Hopf Bifurcation of Stationary Solution of a Delay Equation

In this paper we investigate a Logistic equation with delay and it is shown that if b(x) > c(x), the stationary solution is globally asymptotically stable; if τ is small, U(x) is locally stable; if b(x) < c(x). there is Hopf bifurcation from U(x).     

具有无穷时滞中立型积分微分方程周期解的存在性、唯一性和稳定性

证明了一类具有无穷时滞的中立型积分微分方程解的一致有界性、一致稳定性、周期解的存在唯一性,推广和改进了王全义关于“无穷时滞的积分微分方程的周期解的存在性、唯一性与稳定性”的有关结果。     

时滞微分方程定常解稳定性改变的几何判别法

针对一类系数含时滞的时滞微分方程,讨论了时滞对微分方程定常解稳定性的影响,建立了定常解稳定性发生改变的几何判别法.     

一类非线性微分方程周期解及全局稳定性

本文研究下面一类非线性微分方程dsdt=1 -s- x1 s0 δQ2 ( m1 s0 sk1 s0 s-k)dx1 dt =x1 Q( m1 s0 sk1 s0 s-k) -x1 -x2m2 x1 /Qk2 x1 /Qdx2dt =x2Qm2 x1 /Qk2 x1 /Q -x2　　如果条件m2 x 2 (k1 δ s0 δ-Qλ2 -x 2 ) 2 >m1 δk1 (k2 Q2 λ2 ) 2成立时 ,系统在Ω内存在周期解 ;如果条件m2 x 2 (k1 δ s0 δ -Qλ2 -x 2 ) 2 相似文献   

N(t) = N(t) [a(t)-sum from i=1 to n (b_i(t)N~i(t-τ_i(t)))]的周期正解(英文)

用非线性分析的方法讨论了方程N（t）=N（t）[a（t）－bi（t）Ni（t-τ（t））周的周期正待的存在性，所获结果包含或推广了已有的几个结论[2，3]．     

The Lambert Function on the Solution of a Delay Differential Equation

Recently, a new method for computing the analytical solution of a delay differential equation was developed considering a constant initial function. It is based on the existence of a specific class of polynomials in the delay. In this article, we extend this new method to the case of a continuous initial function. We also show the relationship between the new solution's method and the solution expressed in terms of the Lambert function.     

关于一类时滞Dulling型方程的周期解注记

利用重合度理论研究一类Duffing型方程的周期解问题，获得了有关周期解存在性的新的结果．     

关于一类时滞Duffing型方程的周期解注记

利用重合度理论研究一类Duffing型方程的周期解问题,获得了有关周期解存在性的新的结果.     

关于一个二阶非线性中立时滞微分方程的非振荡解的存在性

A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.     

随机延迟微分方程的Milstein方法的非线性均方稳定性

本文针对一般的非线性随机延迟微分方程,证明了当系统理论解满足均方稳定性条件时,则当方程的漂移和扩散项满足一定的条件时,Milstein方法也是均方稳定的.数学实验进一步验证了我们的结论.     

一类高阶中立型泛函微分方程周期解

本文利用重合度理论讨论了一类高阶中立型泛函微分方程周期解的存在性,获得了若干结论.     

The H-stability of the Solution for Infinite Delay Functional Differential Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＮｏｗａｄａｙｓ，ｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｅｉｎｆｉｎｔｅｄｅｌａｙｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｑｕａｔｉｏｎｈａｓｄｅｖｅｌｏｐｅｄｄｅｅｐｌｙ．Ｍａｎｙｌｉｔｅｒａｔｕｒｅｓｈａｖｅｂｅｅｎｃｏｎｃｅｒｎｅｄｆｏｒｒｅｓｅａｒｃｈｔｈｅｉｎｔｅｇｒａｌｄｉｆｆｅｒｅｎｔｉａｌｑｕａｔｉｏｎａｓｆｏｌｌｏｗｓｘ（ｔ）＝－ａ（ｔ）ｘ（ｔ）＋∫ｔ－∞ｋ（ｔ，ｓ－ｔ，ｘ（ｓ））ｄｓ．（１）　　Ｉｎｏｒｄｅｒｔｏｓｔｕｄｙｔｈｅｉｎｆｉｎｉｔｅｄ…     

一类三阶泛函微分方程周期解的存在唯一性

利用重合度理论研究了一类三阶泛函微分方程x′′′(t)+multiply from i=1 to 2[a_ix~((i))+b_ix~((i))(t-τ_i)]+ g_1(x(t))+g_2(x(t-τ))=p(t)的2π-周期解问题,获得了该方程2π-周期解存在唯一性的若干新结论.