Wave speed and critical patch size for integro-difference equations with a strong Allee effect
Wave speed and critical patch size for integro-difference equations with a strong Allee effect
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DOI：
10.1007/s00285-022-01814-3
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发表时间：
2022-11-01
影响因子：
1.9
通讯作者：
Otto, Garrett
中科院分区：
文献类型：
--
作者：
Li, Bingtuan;Otto, Garrett
给出了具有强Allee效应和无界生境的积分差分方程波速存在性和正性的简化条件。利用这些结果得到了有界生境方程的临界斑块大小的存在性。结果表明，当波速为正时，存在一个临界斑块大小，使得在栖息地大小大于该临界斑块大小时，解在空间中持续存在；当波速为负时，解总是趋近于零。给出了用拉普拉斯扩散核计算临界斑块大小的解析积分公式，该公式证明了多重平衡解的存在性。数值模拟显示了波速、临界斑块大小和Allee阈值之间的关系。
Simplified conditions are given for the existence and positivity of wave speed for an integro-difference equation with a strong Allee effect and an unbounded habitat. The results are used to obtain the existence of a critical patch size for an equation with a bounded habitat. It is shown that if the wave speed is positive there exists a critical patch size such that for a habitat size above the critical patch size solutions can persist in space, and if the wave speed is negative solutions always approach zero. An analytical integral formula is developed to determine the critical patch size when the Laplace dispersal kernel is used, and this formula shows existence of multiple equilibrium solutions. Numerical simulations are provided to demonstrate connections among the wave speed, critical patch size, and Allee threshold.