Spreading in a Shifting Environment Modeled by the Diffusive Logistic Equation with a Free Boundary
Spreading in a Shifting Environment Modeled by the Diffusive Logistic Equation with a Free Boundary
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DOI：
10.1007/s10884-017-9614-2
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发表时间：
2017-08
影响因子：
1.3
通讯作者：
Yihong Du;Lei Wei;Ling Zhou
中科院分区：
文献类型：
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作者：
Yihong Du;Lei Wei;Ling Zhou
我们通过一个具有自由边界的扩散Logistic方程模型研究了环境变化对入侵物种扩散的影响。当环境是均匀和有利的，这个模型首先在Du和Lin（SIAM J Math Anal 42：377-405，2010）中研究，其中为物种的长期动态建立了一个扩散消失二分法，当扩散发生时，它表明物种以某种唯一确定的渐近速度侵入新的领土。在这里，我们考虑这样一种情况，即这种环境的一部分变成不利的，并且环境的不利范围迅速地移动到有利部分。我们证明了，当，物种总是在长期内灭绝，但当，物种的长期行为是由一个由（a）消失，（B）边界蔓延，或（c）蔓延描述的一个分割决定。如果初始种群被写成具有固定参数的形式，则存在使得消失发生在时，边界扩散发生在时，扩散发生在时。
We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is homogeneous and favourable, this model was first studied in Du and Lin (SIAM J Math Anal 42:377–405, 2010), where a spreading–vanishing dichotomy was established for the long-time dynamics of the species, and when spreading happens, it was shown that the species invades the new territory at some uniquely determined asymptotic speed. Here we consider the situation that part of such an environment becomes unfavourable, and the unfavourable range of the environment moves into the favourable part with speed. We prove that when, the species always dies out in the long-run, but when, the long-time behavior of the species is determined by a trichotomy described by (a)vanishing, (b)borderline spreading, or (c)spreading. If the initial population is written in the formwithfixed anda parameter, then there existssuch that vanishing happens when, borderline spreading happens when, and spreading happens when.