弱竞争情形下气候变迁中入侵物种与本地物种的自由边界模型

中文摘要 AI 辅助

我们研究一个扩散的Lotka-Volterra竞争系统的自由边界问题，该系统描述了一个新物种入侵到本地竞争者的栖息地，而该栖息地因气候变化以恒定速度$c>0$从不利环境转变为有利环境。只有入侵者感受到环境的变化，且只有其分布范围受Stefan型自由边界控制，而本地物种占据整个半直线。我们全程在弱竞争机制下工作，在该机制中两个物种可以共存。我们证明了传播-消失二分法：要么入侵者传播且该对收敛到共存稳态$(u^*,v^*)$，要么入侵者消失且本地物种恢复其承载能力。在消失情形下，我们得到显式界限$\lim_{t\to\infty}h(t)\le\frac{\pi}{2}\sqrt{d_1c_2/(a_1c_2-a_2c_1)}$，并给出保证每种情形的判据。当传播发生时，我们确定精确的渐近传播速度：$\lim_{t\to\infty}h(t)/t=\min\{c,c_0\}$，其中$c_0$是对应齐次弱竞争系统的传播速度。特别地，入侵既被竞争者减缓也被气候变迁减缓，而两个机制中较慢的那个决定速度。数值模拟说明了这些结果。

英文摘要

We study a free boundary problem for a diffusive Lotka--Volterra competition system describing the invasion of a new species into the habitat of a native competitor, where habitat suitability shifts from unfavourable to favourable at a constant speed $c>0$ due to climate change. Only the invader is affected by the shifting environment and only its range is governed by a Stefan-type free boundary, while the native species occupies the whole half line. We work throughout in the weak competition regime, in which the two species may coexist. We prove a spreading--vanishing dichotomy: either the invader spreads and the pair converges to the coexistence steady state $(u^*,v^*)$, or the invader vanishes and the native species recovers its carrying capacity. In the vanishing case we obtain the explicit bound $\lim_{t\to\infty}h(t)\le\fracπ{2}\sqrt{d_1c_2/(a_1c_2-a_2c_1)}$, and we give criteria guaranteeing each alternative. When spreading occurs, we determine the exact asymptotic spreading speed: $\lim_{t\to\infty}h(t)/t=\min\{c,c_0\}$, where $c_0$ is the spreading speed of the corresponding homogeneous weak competition system. In particular the invasion is slowed down both by the competitor and by the climate shift, and the slower of the two mechanisms is the one that determines the speed. Numerical simulations illustrate the results.

发表机构

• Ho Chi Minh City University of Technology (HCMUT)（胡志明市理工大学）
• Vietnam National University, Ho Chi Minh City（越南胡志明市国家大学）
• FPT University（FPT大学）
• University of Economics and Law（经济与法律大学）

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