ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＳＩＮＧＬＥＰＯＰＵＬＡＴＩＯＮＭＯＤＥＬＳＷＩＴＨＡＬＭＯＳＴＰＥＲＩＯＤＩＣＥＮＶＩＲＯＮＭＥＮＴＨｅＣｈｏｎｇｙｏｕ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｔｙ）（何崇佑）南京大学，邮编：２１０００８Ａｂ...     

人口动力学中一类含时滞周期反应—扩散方程的正周期解分歧

本文研究人口动力学中一类含时滞周期反应-扩散方程的正周期解问题;利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。     

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process.The uniqueness of the periodic solution is also given.     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

DISCONTINUOUS FORCING OF PERIODIC SOLUTIONS IN C1 VECTOR FIELDS WITH APPLICATIONS TO POPULATION MODELS

Averaging methods are used to compare solutions of two-dimensional systems of ordinary differential equations with constant or periodic forcing. The asymptotic separation of solutions of the periodically forced equations from the solutions of the constantly forced equations is proportional to the L¹ norm of the periodic forcing terms. This result is applied to population models of Kolmogorov-type with climax fitness functions where forcing represents stocking or harvesting of a population. The asymptotic behavior of such systems may be controlled, to some extent, by varying the period and/or amplitude of the forcing functions.     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

In this paper, we establish the existence of a positive periodic solution for a periodic delay single species population growth model, and obtain sufficient conditions for the periodic solution to be globally attractive.     

有食饵补充的二维捕食食饵模型的周期解与概周期解

对于有食饵补充的非定常二维捕食食饵模型，利用微分不等式，讨论了周期解的存在性及其全局吸收性，概周期解的存在性及其在壳扰动不的稳定性。     

THE PERTURBATION OF ALMOST PERIODIC SOLUTION OF ALMOST PERIODIC SYSTEM

By using the exponential dichotomy and the averaging method,a perturbation theoryis established for the almost periodic solutions of an almost differential system.Suppose that the almost periodic differential system(dx)/(dt)=f(x,t) ε~2g(x,t,ε)(1)has an almost periodic solution x=x_0(t,M)for ε=0,where M=(m_1,…,m_k)is theparameter vector.The author discusses the conditions under which(1)has an almostperiodic solution x=x(t,ε)such that x(t,ε)=x_0(t,M)holds uniformly.The results obtained are quite complete.     

带阻尼项的脉冲系统的周期解

本文利用变分法研究了带阻尼项的脉冲系统的周期解.采用一种新的方法,在一些条件下证明了带周期边界条件的脉冲系统存在临界点.本文不仅推广了已有的结果而且还丰富了研究脉冲系统的方法.     

THE PERIODIC SOLUTIONS FOR TIMEDEPENDENT AGE-STRUCTURED POPULATION MODELS

1IntroductionTl1eage-structuredpopulationmodelhasbeensuccessfullyusedinpopulationdynamics['f'].Tl1egeneralage-structuredpopuIationmodelisdescribedbythefollowingpartialdifferentialequatiolls{3]:whereu(a,f)istheage-specificdensityofasingleage-structuredspeciesattimet,p(a,f)andb(a,t)aretheage-specificpercapitaldeathrateandbirthrateofthespeciesattimet,respectively.TherealAisthemaxinlulllageforanyindividuali11thepopulation,and[A1,A2listhefecundityperiodoffelllales.Thefunctiolluo(a)istheinitialdel…     

STABLE PERIODIC BEHAVIOR IN A PIONEER-CLIMAX MODEL

Two dimensional pioneer-climax models of differential and difference equations are presented and analyzed. An effort is made to separate a species response to density from the competitive effects. Stable periodic behavior is established for both models via Hopf bifurcation. For the differential equation model, a general formula is presented for determining the stability of the bifurcating period orbit.     

一类具有非线性扩散和时滞的捕食系统的持续性与周期解

研究了一类具有非线性扩散和Beddington-Deangelis功能性反应,且同时具有连续时滞和离散时滞的非自治两食饵一捕食者系统,证明了在适当条件下该系统是一致持久的,并且得到了系统正周期解全局渐近稳定的充分条件.最后,给出一个例子以说明得到的结果.     

多种产品生产系统的生产计划问题

研究一个为满足确定性需求而进行产品生产的系统.系统中有一台用于生产的机器, 生产$n$种不同的产品.每一种产品都有确定的日需求. 我们将能够满足所有产品需求的生产计划称之为可行计划.主要想通过数学模型, 来建立一套判定可行计划存在性的理论. 在确保存在可行计划的前提下, 设计了一种找寻出具体可行计划的计算方法. 并且, 进一步可以通过0-1规划来优化系统的效率,称之为最小化产能占用率.     

PERIODIC REACTION AND TURBULENCE OF CHEMICAL BRUSSELATOR

In this paper,we discuss the reaction model of tri-molecules and the exi- stence of periodic reaction under certain original density conditions of two ob- jects without diffusion phenomena.We prove that the periodic reaction exhibit some chemical phenomena that violate the second law of thermo-mechanics. Finally,we research similar properties and phenomena concerning Belousov- Zhabotinsky reaction model.     

PERMANENCE,PERIODIC AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS STAGE STRUCTURED POPULATION DYNAMICS WITH TIME DELAY AND DIFFUSION

A nonautonomous stage-structured two species model with time delay anddiffusion is considered. It is shown that the system is uniformly persistent undersome conditions. By discussing the independent subsystem, more brief sufficientconditions are drawn for a unique positive periodic solution which is globallyattractive and the existence of the positive almost periodic solution which isuniformly asymptotically stable by the Razumikhin function method.     

高维时滞周期的Kolmogorov型系统的正周期解

本文应用Ｂａｎａｃｈ空间中的Ｈｏｒｎ不动点得到了高维时滞的周期Ｋｏｌｍｏｇｏｒｏｖ型生态系统的正周期解存在性定理,作为这个定理的应用,讨论了几类时滞的周期ＬｏｔｋａＶｏｌｔｅｒｒａ型系统的正周期解的存在性问题,建立了新的实用的判别准则。     

一种广义周期Besov类的多元周期多项式样条逼近

本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间．给出了广义周期Besov类的一种推广，得到了空间元素的一种表示定理，不仅给出了一种多元周期多项式样条算子．而且证明了所得的结果．     

ON THE EXISTENCE OF PERIODIC SOLUTION OF HIGHER ORDER PERIODIC SYSTEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＨＩＧＨＥＲＯＲＤＥＲＰＥＲＩＯＤＩＣＳＹＳＴＥＭ（王全义）华侨大学，邮编：３６２０１１ＷａｎｇＱｕａｎｙｉ（ＨｕａｑｉａｏＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...     

两种群非自治Lotka-Volterra竞争扩散系统的概周期解

本文讨论两种群概周期竞争扩散系统，利用微分不等式，证明了系统概周期解的存在、唯一性及其在壳扰动下的稳定性．     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…