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<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>

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The role of random perturbations in the dynamic variability of a discrete predator–prey model: a stochastic sensitivity analysis

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Irina Bashkirtseva,
  • Lev Ryashko

摘要

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.