{"title":"The role of random perturbations in the dynamic variability of a discrete predator-prey model: a stochastic sensitivity analysis.","authors":"Irina Bashkirtseva, Lev Ryashko","doi":"10.1007/s00285-025-02213-0","DOIUrl":null,"url":null,"abstract":"<p><p>A problem of identification and mathematical analysis of stochastically-induced qualitative changes in nonlinear population dynamics is considered. We study this problem on the base of a discrete prey-predator model with the Holling type II functional response. Even in the deterministic case, this model exhibits a rich regular and chaotic behavior, including bistability. We study different noise-induced scenarios with transitions between regimes of persistence and extinction. In this study, we show a key role of geometry of basins of attraction and specific chaotic transients. In parametric analysis of the noise-induced extinction, the stochastic sensitivity technique and confidence domains method are used. This new mathematical method sheds light on the intrinsic mechanisms of noise-induced phenomena in population dynamics. We show how random fluctuations in the parameter of predator growth rate contract persistence zones of both prey and predator.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 5","pages":"50"},"PeriodicalIF":2.3000,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Biology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00285-025-02213-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
A problem of identification and mathematical analysis of stochastically-induced qualitative changes in nonlinear population dynamics is considered. We study this problem on the base of a discrete prey-predator model with the Holling type II functional response. Even in the deterministic case, this model exhibits a rich regular and chaotic behavior, including bistability. We study different noise-induced scenarios with transitions between regimes of persistence and extinction. In this study, we show a key role of geometry of basins of attraction and specific chaotic transients. In parametric analysis of the noise-induced extinction, the stochastic sensitivity technique and confidence domains method are used. This new mathematical method sheds light on the intrinsic mechanisms of noise-induced phenomena in population dynamics. We show how random fluctuations in the parameter of predator growth rate contract persistence zones of both prey and predator.
期刊介绍:
The Journal of Mathematical Biology focuses on mathematical biology - work that uses mathematical approaches to gain biological understanding or explain biological phenomena.
Areas of biology covered include, but are not restricted to, cell biology, physiology, development, neurobiology, genetics and population genetics, population biology, ecology, behavioural biology, evolution, epidemiology, immunology, molecular biology, biofluids, DNA and protein structure and function. All mathematical approaches including computational and visualization approaches are appropriate.