ArticleScientific reports2018
Asymptotic stability of a modified Lotka-Volterra model with small immigrations.
Article in Scientific reports, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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8 citing papers in PubMed.
- Effects of Seasonal Births and Predation on Disease Spread.Bulletin of mathematical biology · 2026Article
- Seasonal trophic controls drive population variability in a foundational marine copepod.Scientific reports · 2025Article
- Stability and robustness of kinetochore dynamics under sudden perturbations and stochastic influences.Scientific reports · 2025Article
- Aggregated Distribution as an Explanation for the Paradox of Plankton and Collective Animal Behavior.Biology · 2022Article
- Establishing an inexpensive, space efficient colony ofJournal of applied entomology = Zeitschrift fur angewandte Entomologie · 2022Article
- The Stochastic Nature of Functional Responses.Entropy (Basel, Switzerland) · 2021Article
- Stochastic dynamics of predator-prey interactions.PloS one · 2021Article
- Forecasting of landslide displacements using a chaos theory based wavelet analysis-Volterra filter model.Scientific reports · 2019Article
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14 authors.
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Abstract
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.
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