文章基本信息

标题：Asymptotic stability of a modified Lotka-Volterra model with small immigrations
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作者：Takeru Tahara ; Maica Krizna Areja Gavina ; Takenori Kawano 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2018
卷号：8
期号：1
页码：7029
DOI：10.1038/s41598-018-25436-2
语种：English
出版社：Springer Nature
摘要：Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.