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1.
The Gierer-Meinhardt's Model with a time delaydx(t)/dt=Co-bx(t)+cx2(t-τ)/y(t)(1+kx2(t-τ)),dy(t)/dt=x2(t)-ay(t).is studied. It is proved that there exists a Hopf bifurcation. Some conditions are established under which the equilibrium is globally stable.  相似文献   

2.
具有正负系数的中立型方程的振动性   总被引:7,自引:0,他引:7  
讨论中立型方程d/dt[x(t)-R(t)x(t-r)] P(t)x(t-t)-Q(t)x(t-δ)=0,(*)其中P,Q,R∈C[(to,∞),R∧ ),r,τ,δ∈(0,∞),τ≥δ,在允许R(t) ∫∧tt=τ δQ(u)du-1变号的情况下得到(*)的所有解振动的判据。  相似文献   

3.
本文证明了中立型微分差分方程d/(dt)[x(t)+cx(t-τ)]=ax(t)-ax(t-τ),|c|<1,其中a,c,τ为常数,τ≥0,与常微分方程 d/(dt)x(t)=0稳定性等价时,滞量τ所满足的充分必要条件是0≤τ<△(a,c),这里(?)  相似文献   

4.
蒋建初 《数学杂志》2002,22(3):277-280
考虑二阶中立型时滞微分方程[a(t)|(x(t) p(t)x(t-τ))′|^α-1(x(t) p(t)x(t-τ))′]′ f(t,x(t-σ))=0(E)其中α,τ,σ是非负常数,a(t),p(t)∈C([t0,∞),R),f(t,x)∈C(R,R)。建立了方程(E)的一些新的振动条件。  相似文献   

5.
杜瑞霞  刘萍  罗泳 《数学研究》2010,43(1):1-10
我们研究下面具有反馈控制和参数的非线性微分系统的正周期解的存在性与不存在性:{dx/dt=-r(t)x(t)+λF(t,xt,u(t-δ(t))),du/dt=-h(t)u(t)+g(t)x(t-σ(t)).在一定条件下通过应用Leggett.Williams不动点定理,证明该系统至少有三个正周期解;在另外的条件下,通过用反证法证明了该系统的正周期解不存在.  相似文献   

6.
捕食模型正周期解存在性的一个注记   总被引:1,自引:0,他引:1  
利用重合度理论中的延拓定理讨论了多滞量捕食模型(dN_1(t))/dt=N_1(t)[r_1(t)-a_(11)(t)N_1(t-τ_1(t))-a_(12)(t)N_2(t-τ_2(t))] (dN_2(t))/dt=N_2(t)[-r_2(t)+a_(21)(t)N_1(t-τ_3(t))]的正周期解的存在性,得到了保证上述系统周期解存在的一组时滞依赖的充分条件,补充和完善了已有学者的工作.  相似文献   

7.
运用k-集压缩算子的拓扑度抽象连续定理,研究了如下一类高阶微分方程的周期解存在性问题x(m)(t)= r(t)-a(t)x(t-σ)-b(t)x(m)(t-τ).并将其应用于研究一类中立型对数种群模型dN/dt= N(t) [r(t)-a(t) In N(t-σ-b(t)d/(dt)In N(t-τ)]的正周期解存在性...  相似文献   

8.
在[1]中,笔者用标量函数的方法研究了具有分解形式(dX_i)/(dt)=G_i(X_i,t) sum from i=1 j(?)i to r A_(ij)(t)X_j(t) sum from j=1 to r B_(ij)(t)[X_j(t-τ(ij))-X_j(t)](i=1,2,…,r)的复合系统(dX)/(dt)=H[t,X(t),X(t-τ)]及具有分解形式  相似文献   

9.
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation dN/dt=N(t)[a(t)-β(t)N(t)-b(t)N(t-a(t))-c(t)N(t-τ(t))]  相似文献   

10.
本文考虑变系数变时滞的Hopfield神经网络系统dxi/dt=-bi(t)xi(t) ∑^nj=1aij(t)fj(λjxj(t-τij(t))) Ii(t)的全局惭近稳定性,获得了一个充分条件。  相似文献   

11.
12.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

13.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

14.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

17.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

18.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

19.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

20.
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

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