具有非局部效应的时滞SEIR系统的周期行波解

该文研究了一类具有非局部效应和非线性发生率的时滞SEIR系统的周期行波解.首先,定义基本再生数R₀并构造适当的上下解,将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题,利用Schauder不动点定理结合极限理论建立该系统周期行波解的存在性.其次,利用反证法结合比较原理,建立当基本再生数R₀<1时该系统周期行波解的不存在性.     

带有外部输入项的时间周期SIR传染病模型的周期行波解北大核心CSCD

研究了一类带有外部输入项的时间周期SIR传染病模型周期行波解的存在性和不存在性.首先,通过构造辅助系统适当的上下解并定义闭凸锥,将周期行波解的存在性转化为定义在这个闭凸锥上的非单调算子的不动点问题,利用Schauder不动点定理建立辅助系统周期解的存在性,并利用Arzela-Ascoli定理证明了原模型周期行波解的存在性.其次,借助分析技术得到了周期行波解的不存在性.     

Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems北大核心CSCD

该文研究了一类格竞争系统的双稳周期行波解的存在性.首先,将两种群竞争系统转化为合作系统;其次,构造合作系统的上下解,并建立比较原理,得到当初始函数满足一定条件时,解在无穷远处是收敛的;最后,利用黏性消去法证明系统连接两个稳定周期平衡点的行波解的存在性.     

一类具有扩散项的流行性传染病模型中的行波解

讨论了一类具有扩散项的流行性传染病模型中的行波解的存在性.首先,将对该模型所对应的反应扩散系统的行波解的讨论转化为对二阶常微分系统的上下解的讨论;然后,通过上下解方法建立了这个具有扩散项的传染病模型中行波解的存在性条件,并进一步讨论了扩散因素对行波解的波速的影响,得到被感染人群的流动对病毒的传播有一定的影响.     

一类具有时滞和空间扩散的SIR传染病模型的行波解

研究了一类具有时滞和空间扩散的SIR传染病模型,通过分析相应的特征方程,讨论了系统每个平衡态的局部稳定性,通过运用交叉迭代方法和Schauder不动点定理,把行波解的存在性转化为一对上下解的存在性,通过构造一对上下解,得到了连接无病平衡态和地方病平衡态的行波解的存在性.     

三物种竞争-扩散系统双稳行波解的波速符号

在双稳竞争-扩散模型中,由于行波解的波速符号可以预测哪些物种更具有优势并最终占据整个栖息地,因此研究行波解的波速符号具有重要的生物学意义.首先将三物种种群Lotka-Volterra竞争-扩散系统转化为合作系统.然后运用比较原理得到双稳波速与波廓方程特定上下解波速的比较原理.最后根据比较原理以及构造合适的上下解,得到一些判断双稳行波解波速符号的充分条件.这些结果能够更好地预测和控制生物种群的竞争结果.     

一类时间周期的时滞竞争系统行波解的存在性

该文研究了一类时间周期的时滞Lotka-Volterra竞争系统的行波解.首先,通过构造适当的上、下解,结合单调迭代的方法证明了当cc~*时,存在连接两个半正周期平衡点的行波解,并且利用比较原理得到了周期行波解关于z的单调性.其次,通过单调性证明了行波解在正、负无穷远处的渐近行为.最后,证明了当c=c~*时周期行波解的存在性.     

中立型反应扩散方程的波前解

关于时滞反应扩散方程行波解的结果很多,但中立型时滞反应扩散方程行波解的研究却很少,在反应项是拟单调的条件下,通过定义上下解和构造单调迭代序列,得到了中立型时滞反应扩散方程波前解的存在性.     

Banach空间二阶周期边值问题的一种拟上下解方法

利用比较结果,通过构造L-拟上下解的单调迭代过程,在L-拟上下解反序的情形下,研究了Banach空间二阶周期边值问题解的存在性,并获得该问题解的存在性与唯一性结果.     

带非局部扩散项的一般性霍乱模型的行波解

该文研究一类具有一般性的带非局部扩散项的霍乱模型,用不同的函数表示人与人之间以及人与环境之间的发生率,以及霍乱病菌的增长函数.当R₀>1,c>c^*时,通过构造上下解函数,结合Schauder不动点定理讨论该模型行波解的存在性,再构造Lyapunov函数讨论行波解的渐近性.当c*时,通过双边拉普拉斯变换和Fatou引理证明该模型行波解的不存在性.     

Travelling waves in an infectious disease model with a fixed latent period and a spatio–temporal delay

This paper is concerned with the existence of travelling waves to an infectious disease model with a fixed latent period and a spatio–temporal delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this model is discussed. By constructing a pair of upper–lower solutions, we use the cross iteration method and the Schauder’s fixed point theorem to prove the existence of a travelling wave solution connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.     

Travelling waves of a three-species Lotka–Volterra food-chain model with spatial diffusion and time delays

This paper is concerned with the existence of travelling wave solutions to a three-species Lotka–Volterra food-chain model with spatial diffusion and time delays. By using the cross iteration method and Schauder’s fixed point theorem, we reduce the existence of travelling wave solutions to the existence of a pair of upper–lower solutions which are easy to construct in practice. Numerical simulations are carried out to illustrate the main results.     

Coinvasion–coexistence travelling wave solutions of an integro-difference competition system

This paper is concerned with the travelling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion–coexistence process of two competitors with age structure. The existence of non-trivial travelling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and non-existence of travelling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle.     

Bistable travelling waves in competitive recursion systems

This paper is devoted to the study of spatial dynamics for a class of discrete-time recursion systems, which describes the spatial propagation of two competitive invaders. The existence and global stability of bistable travelling waves are established for such systems under appropriate conditions. The methods involve the upper and lower solutions, spreading speeds of monostable systems, and the monotone semiflows approach.     

Travelling waves of a delayed SIRS epidemic model with spatial diffusion

This paper is concerned with the existence of travelling waves to an SIRS epidemic model with bilinear incidence rate, spatial diffusion and time delay. By analysing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder’s fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave solution connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results.     

Travelling Waves for Reaction Diffusion Equations

In this paper the travelling waves for the reaction diffusion equation in most general case is considered. The existence of travelling wave solutions is proved under very weak conditions, which are also necessary for the nonlinear term. A difference method is suggested and Leray-Scbauder fixed point theorem is used to prove the existence of discrete travelling waves. Then the convergence is shown and so the solution for the differential equation is obtained.     

Reaction-Diffusion Equations in Homogeneous Media: Existence,Uniqueness and Stability of Travelling Fronts

The goal of this survey is to describe the construction and some qualitative properties of particular global solutions of certain reaction-diffusion equations. These solutions are known as travelling fronts (or travelling waves) and play an important role in the long-time behaviour of the solutions of the parabolic system. We will mainly focus on the existence of travelling wave solutions and their stability. We will also give some standard tools in elliptic and parabolic theory, which are of general interest.     

New type of travelling wave solutions

We study the existence of combustion waves for an autocatalytic reaction in the non‐adiabatic case. Based on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of travelling waves solutions, the so‐called canard travelling waves. Copyright © 2003 John Wiley & Sons, Ltd.     

广义特殊Tzitzeica-Dodd-Bullough类型方程的行波解

本文研究了广义特殊Tzitzeica-Dodd-Bullough类型方程,利用动力系统分支理论方法,证明该方程存在周期行波解,无界行波解和破切波解,并求出了一些用参数表示的显示精确行波解.