Persistence for a Two-Stage Reaction-Diffusion System
Persistence for a Two-Stage Reaction-Diffusion System
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DOI：
10.3390/math8030396
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发表时间：
2020-03
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影响因子：
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通讯作者：
R. S. Cantrell;C. Cosner;Salomé Martínez
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文献类型：
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作者：
R. S. Cantrell;C. Cosner;Salomé Martínez
在这篇文章中，我们研究了异质环境中阶段结构种群的反应扩散模型中的扩散速率如何影响模型对种群持续生存或灭绝的预测。在没有阶段结构的种群中，更快的扩散通常是有害的。相反，我们发现，在阶段性结构的人群中，这可能是有害的，也可能是有益的。如果成体可以繁殖的区域与幼体可以成熟的区域相同，通常会有利于较慢的扩散，但如果这两个区域分开，则可能有利于较快的扩散。我们的分析主要包括线性化系统在(0，0)附近的主特征值的估计以及它们在大或小扩散速率下的渐近行为。我们研究的模型一般不是合作系统，但如果成年人只与其他成年人竞争，青少年与其他青少年竞争，那么它就是合作系统。在这种情况下，合作系统的一般理论意味着，当模型预测持久性时，它存在唯一的正均衡。在这种情况下，我们得到了关于小扩散和大成虫生育率正平衡点的渐近行为的一些结果。
In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model’s predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around ( 0 , 0 ) and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case.