被捕食者带有第三边值的捕食模型的正稳态解的存在性

该文研究了一类被捕食者带有第三边值的捕食模型. 首先获得了它存在正稳态解的充要条件是a>mb+d₁λ₁; 然后研究了它的正稳态解的局部稳定性和唯一性;最后讨论了充分大的扩散参数对它的正稳态解的存在性的影响.     

一类捕食-被捕食模型的正平衡解存在性

针对自然界中捕食者染病的现象,建立了捕食者染病的捕食-被捕食模型,研究了捕食者为躲避疾病进行扩散,并且具有HollingⅡ功能性反应函数和齐次Neumann边界条件的问题,利用Harnack不等式和最大值原理给出反应扩散问题的正平衡解的先验估计,并利用拓扑度理论证明该问题的非常数正平衡解的存在性.讨论了对应平衡态问题的非常数正平衡解存在性。     

一类带有扩散的三种群捕食模型的非常数正平衡解

一类带有扩散和非单调比率依赖响应函数的捕食模型在某些条件下有两个正常数解,讨论了该捕食模型在齐次Neumann边界条件下的非常数正平衡解的存在性和不存在性.     

具有两食饵趋向的食物链模型古典解的全局存在性

本文探讨在留曼边界条件下带有两食饵趋向和功能Ⅱ反应函数的三物种食物链模型,此模型的主要特征是捕食者捕食速度空间上的临时变化是由食饵的梯度决定的.应用压缩原理,抛物方程的Schauder估计和Lp估计,证明了此模型古典解的全局存在性.     

具阶段结构的非自治捕食模型的持久性

讨论了一类具有密度制约且食饵带有阶段结构和捕食者仅捕食成年食饵的捕食-食饵种群模型,,得到了持久生存以及非平凡周期解存在的充分条件.     

具有Holling-II型功能反应和交叉扩散的捕食-食饵模型正平衡解的存在性和不存在性

本文主要研究一类在齐次Dirichlet边界条件下带交叉扩散的Holling-II型捕食者-食饵模型正平衡解的存在性, 其中两个交叉扩散系数分别代表食饵远离捕食者的趋势和捕食者追逐食饵的趋势. 应用不动点指标理论得到了正平衡解存在的充分条件, 并进一步研究了正平衡解不存在的条件.     

一个具有扩散和比例依赖响应函数捕食模型的定性分析

本文考虑了一个具有扩散项和比例依赖响应函数的捕食模型. 该模型带有齐次Neumann边界条件. 本文主要关心该反应扩散系 统解的大时间行为及其对应的平衡态问题. 首先通过构造各种Lyapunov函数, 讨论 唯一的正常数平衡解的全局稳定性. 然后, 对于平衡态问题, 建立了正平衡解上下界 的先验估计, 并且导出了当物种的扩散系数很大或者很小时非常数正平衡解的一些不存在性结果.     

捕食者带有疾病的入侵反应扩散捕食系统的空间斑图

本文考察了一类在有界区域内在零流边界条件下捕食者带有疾病的入侵反应扩散捕食系统.在没有入侵反应扩散的条件下考虑了这类系统的局部和全局稳定性.找到了具有入侵反应扩散系统的非常数定态解存在性和不存在性的充分条件,其存在预示着空间斑图的形成.文中结论表明当物种的生存空间很大,捕食者的捕食趋向很小时,没有空间斑图出现,两物种不能共存且没有疾病广泛传播.当入侵反应扩散系数很大,自扩散系数固定时,空间斑图出现,两物种能共存,这时疾病也广泛存在.     

带有脉冲和Holling-Ⅳ型功能反应函数的中立型捕食-食饵模型的周期解

该文研究一类带有中立型脉冲时滞和Holling-Ⅳ型功能反应函数的捕食-食饵模型.通过运用Mawhin迭合度理论和分析技巧,得到了捕食-食饵模型正周期解存在性的充分条件.     

带有交叉扩散的捕食模型的非常数正稳态解的存在性

本文研究了下列带有交叉扩散的捕食模型的稳态问题的非常数正解的存在性,证明了当d4>1/m1v-u时存在(g1,d2,d3)使得稳态问题存在非常数正解;而当d4≤1/m1v-u或者d1≥m1v-u/u1或者a(m1b,a2(b))时稳态问题不存在非常数正解．     

Multiple positive solutions for a class of semilinear elliptic systems with nonlinear boundary condition

Two positive solutions are obtained for the nonlinear homogeneous system with nonlinear homogeneous boundary condition via the Nehari manifold approach.     

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.     

Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds

In this paper, we consider Hamilton–Jacobi equations with homogeneous Neumann boundary condition. We establish some results on noncompact manifold with homogeneous Neumann boundary conditions in view of weak Kolmogorov‐Arnold‐Moser (KAM) theory, which is a generalization of the results obtained by Fathi under the non‐bounded condition. Copyright © 2014 John Wiley & Sons, Ltd.     

Non-constant positive steady-states of a diffusive predator-prey system in homogeneous environment

In this paper, we investigate the existence and non-existence of non-constant positive steady-states of a diffusive predator-prey interaction system under homogeneous Neumann boundary condition. In homogeneous environment, we show that the predator-prey model with Leslie-Gower functional response has no non-constant positive solution, but the system with a general functional response may have at least one non-constant positive steady-state under some conditions.     

Existence and asymptotic behavior of solutions for a mathematical ecology model with herd behavior

In this work, we consider a prey-predator model with herd behavior under Neumann boundary conditions. For the system without diffusion, we establish a sufficient condition to guarantee the local asymptotic stability of all nontrivial equilibria and prove the existence of limit cycle of our proposed model. For the system with diffusion, we consider the long time behavior of the model including global attractor and local stability, and the Hopf and steady-state bifurcation analysis from the unique homogeneous positive steady state are carried out in detail. Furthermore, some numerical simulations to illustrate the theoretical analysis are performed to expand our theoretical results.     

Positive steady-state solutions of the Noyes–Field model for Belousov–Zhabotinskii reaction

In the paper, we investigate the Noyes–Field model for Belousov–Zhabotinskii reaction and study positive steady-state solutions of this model with the homogeneous Neumann boundary condition. We obtain the existence and non-existence of non-constant positive steady-state solutions.     

Blow-up of a nonlocal semilinear parabolic equation with positive initial energy

In this short work, a semilinear parabolic equation with a homogeneous Neumann boundary condition is studied. A blow-up result for a certain solution with positive initial energy is established.     

A sufficient and necessary condition for the existence of positive solutions for a prey–predator system with Ivlev-type functional response

We deal with a predator–prey interaction model with Ivlev-type functional response which is subject to the homogeneous Dirichlet boundary condition. On the basis of the fixed point index theory, we give a sufficient and necessary condition for the existence of positive solutions of the model.     

Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate

In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.