Global asymptotic stability of Lotka–Volterra 3-species reaction–diffusion systems with time delays
Global asymptotic stability of Lotka–Volterra 3-species reaction–diffusion systems with time delays
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DOI：
10.1016/s0022-247x(03)00033-7
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发表时间：
2003-05
影响因子：
1.3
通讯作者：
C. Pao
中科院分区：
文献类型：
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作者：
C. Pao
研究了三个三种群时滞Lotka-Volterra反应扩散方程组及其相应的无扩散常微分方程组.时滞可以是离散的也可以是连续的，边界条件是Neumann型的。本文的目的是获得一些简单的和容易验证的条件的存在性和全局渐近稳定的正平衡态解的三个模型问题。这些条件只涉及反应速率常数，与扩散效应和时滞无关。全局渐近稳定性的结果表明，三个模型系统共存，是永久的，平凡解和所有半平凡解是不稳定的。我们解决这个问题的方法是基于更一般的反应扩散系统的上下解方法，该方法为3种群模型问题提供了一个通用框架。讨论了两种群竞争和捕食-被捕食反应扩散系统的全局稳定性。
This paper is concerned with three 3-species time-delayed Lotka–Volterra reaction–diffusion systems and their corresponding ordinary differential systems without diffusion. The time delays may be discrete or continuous, and the boundary conditions for the reaction–diffusion systems are of Neumann type. The goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady-state solution for each of the three model problems. These conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays. The result of global asymptotic stability implies that each of the three model systems coexists, is permanent, and the trivial and all semitrivial solutions are unstable. Our approach to the problem is based on the method of upper and lower solutions for a more general reaction–diffusion system which gives a common framework for the 3-species model problems. Some global stability results for the 2-species competition and prey–predator reaction–diffusion systems are included in the discussion.