移动环境下格点–反应扩散系统的动力学分析

Dynamic Analysis of Lattice Reaction-Diffusion Systems with Shifting Environments

摘要: 本文研究了一类格点反应–扩散方程，其中非线性项$f\left(u\right)$ 表示受种群密度影响的死亡率。该类模型常用于研究变化栖息地中物种可持续性与空间传播的相互作用机制。现有的种群动力学研究表明：当$c^{\ast }\left(\infty \right)<c$ 时种群面临灭绝，而当$c^{\ast }\left(\infty \right)>c$ 时种群可持续生存。通过结合解析方法与半群理论，我们在仅要求增长函数$r(\cdot )$ 具有弱符号不变性的条件下，建立了更具普适性的结论。

Abstract: In this paper, we study a class of lattice reaction-diffusion equations, in which the term $f\left(u\right)$ represents mortality influenced by population density. These models are used to study the interplay between species sustainability and spatial propagation in shifting habitats. Current research in population dynamics indicates that a population faces extinction if $c^{\ast }\left(\infty \right)<c$ , but persists when $c^{\ast }\left(\infty \right)>c$ . Through a combination of analytical techniques and semigroup methods, we establish extended results requiring only weak sign-constancy assumption on the growth function $r(\cdot )$ .