TRAVELING WAVES FOR A NONLOCAL DISPERSAL EPIDEMIC MODEL

This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.     

TRAVELING WAVES IN A BIOLOGICAL REACTION-DIFFUSION MODEL WITH STRONG GENERIC DELAY KERNEL AND NON-LOCAL EFFECT

In this paper,we consider the reaction diffusion equations with strong generic delay kernel and non-local effect,which models the microbial growth in a flow reactor.The existence of traveling waves is established for this model.More precisely,using the geometric singular perturbation theory,we show that traveling wave solutions exist provided that the delay is sufficiently small with the strong generic delay kernel.     

具Allee反应的时滞扩散单种群增长模型的波前解

本文利用上、下解技巧和单调迭代法,研究了具Allee反应的时滞扩散单种群增长模型的波前解,给出了波前解存在的条件.     

具Allee反应的时滞扩散单种群增长模型的波前解

本文利用上、下解技巧和单调迭代法,研究了具Allee反应的时滞扩散单种群增长模型的波前解, 给出了波前解存在的条件.     

TRAVELLING FRONT SOLUTIONS IN A DIFFUSIVE VECTOR DISEASE MODEL WITH SPATIO-TEMPORAL DELAY

This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.     

DYNAMICS OF A NONLOCAL DISPERSAL FOOT-AND-MOUTH DISEASE MODEL IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world. It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses. The disease has become a major public health concern. In this paper, we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment, which couples virus-to-animals and animals-to-animals transmission pathways, and investiga...     

SPREADING SPEED IN THE FISHER-KPP EQUATION WITH NONLOCAL DELAY

This paper is concerned with the Fisher-KPP equation with diffusion and non-local delay.Firstly,we establish the global existence and uniform boundedness of sol...     

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution) dispersals:■Here a ≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1) linearized at(Φc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(Φc(ξ),0) as t→-∞,where Φc denotes the traveling wave solution of the nonlocal Fisher-KPP equation u_t     

具无界时滞非自治Logistic模型的全局吸引性(英文)

考虑非自治Ｌｏｇｉｓｔｉｃ模型△ｘｎ ＝ ｐｎｘｎ（１ － ｘｎ－ ｋｎλ）,　　ｎ ＝ ０,１,…, （１）其中｛ｐｎ｝ｎ０为非负实数列,｛ｋｎ｝ｎ０为非负整数列且ｌｉｍｎ→∞（ｎ－ ｋｎ）＝ ∞,ｌｉｍ ｓｕｐｎ→∞ ｋｎ＝ ∞,λ为正常数．我们获得了方程（１）的平衡点λ全局吸引的新的充分条件,改进了文［５］的相应结果．     

具有非线性接触率和时滞的SIRS流行病模型

本文研究了具有非线性接触率βＩ＾ｐｓ／１＋αＩ＾ｑ和恢复类中具有分布时滞的ＳＩＲＳ流行病模型的解的存在性和连续性,正不变集,平衡位置以及平衡位置的稳定性。     

GLOBAL ATTRACTIVITY IN A MODEL OF BOBWHITE QUAIL WITH DELAY

1IlltroductionInl99o,MiltinandB.lairl1]raisedadifferenceequationasapopulationmodelforthegrowthofthebobwhitequailpopulationofnorthernWisconsin.Inl994,Ladas,G.proposedthefollowingopenproblem[']:"(a)Investigatetheboundedness,persistence,permanence,oscillation,periodicity,andglobalattractivity;(b)ExtendEq.(*)byintroducingdelaysintothemodel,andinvestigatethedelayedequation.".Inl996,TangHeng-shengandOuChun-hua[3]considereditsglobalattrac-tivity,partlyansweredaboveopenproblem(a).Inl999,byintrodu…     

一个具有时滞和非线性接触率的传染病模型

本文研究了具有非线性接触率和在恢复类中具有分布时滞的SIRS传染病模型的解的存在性、连续性和平衡位置以及平凡平衡位置的稳定性。     

A DIFFUSIVE SVEIR EPIDEMIC MODEL WITH TIME DELAY AND GENERAL INCIDENCE

In this paper,we consider a delayed diffusive SVEIR model with general inci-dence.We first establish the threshold dynamics of this model.Using a Nonstandard Fi...     

PYRAMIDAL TRAVELING FRONTS OF BISTABLE REACTION-DIFFUSION EQUATIONS WITH DELAY

This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.     

竞争扩散时滞模型的稳定性和Hopf分歧

本文研究一类含扩散的竞争时滞模型的定常解的稳定性以及Ｈｏｐｆ分坡解的存在性,进而给出分歧周期解的稳定性和分歧方向。     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

一类带有扩散和时滞的捕食与被捕食模型的渐近性质

本文中，我们考虑一类带有扩散和时滞的捕食与被捕食系统．我们分析了系统的非负不变性，边界平衡点性质，全局渐近稳定性及永久持续生存性．在这一系统中，当时滞由0变到ro时，系统在平衡点附近发生Hopf分支．即当r增加通过临界值ro时，从正平衡点分支出周期解．     

一类具时滞的生理模型的Hopf分支

本文研究了一类简化的具时滞的生理模型的稳定性和Ｈｏｐｆ分支．首先,以滞量为参数,应用Ｃｏｏｋｅ的方法,把Ｒ＾＋分为两个区间,使当滞量属于相应区间时,所考虑的模型的平凡解是稳定或不稳定的,同时得到了Ｈｏｐｆ分支值．然后,应用中心流形和规范型理论,得到了关于确定Ｈｏｐｆ分支方向和分支周期解的稳定性的计算公式．最后,应用Ｍａｔｈｅｍａｔｉｃａ软件进行了数值模拟。     

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.     

两部门的时滞经济增长模型

本文考虑了存在生产滞后的 Furuno两部门经济增长模型 .给出了此模型资本 -劳动比 k的稳定性和振荡性 ,分析了生产周期时滞对 k稳定性区域的影响 .进一步利用 Hopf分支的方法讨论了 Furuno模型存在周期轨道的条件 .