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

IF 2.3 4区 数学 Q2 BIOLOGY
Irina Bashkirtseva, Lev Ryashko
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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.

随机扰动在离散捕食者-猎物模型动态变异性中的作用:随机灵敏度分析。
研究了非线性种群动态中随机引起的质变的辨识和数学分析问题。我们在一个具有Holling II型函数响应的离散捕食-捕食模型的基础上研究了这个问题。即使在确定性情况下,该模型也表现出丰富的规则和混沌行为,包括双稳定性。我们研究了不同的噪声引起的情景,并在持续和消失之间转换。在这项研究中,我们展示了吸引盆地的几何形状和特定的混沌瞬态的关键作用。在噪声消光的参数分析中,采用了随机灵敏度法和置信域法。这种新的数学方法揭示了种群动力学中噪声诱发现象的内在机制。我们展示了捕食者生长速率参数的随机波动如何收缩了猎物和捕食者的持久区。
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来源期刊
CiteScore
3.30
自引率
5.30%
发文量
120
审稿时长
6 months
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.
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