具有Crowley-Martin型功能反应的捕食者-食饵模型的复杂动力学和随机敏感性分析

摘要/Abstract

摘要：

捕食者与食饵的相互作用在保护物种多样性方面起着关键作用.该文提出了一个具有Crowley-Martin型功能反应的随机捕食者-食饵模型.结果表明，当$λ$ < 0时，捕食者种群有灭绝的趋势，食饵种群的解弱收敛到一个不变的概率分布.当$λ$>0时，发现随机系统存在唯一一个遍历平稳分布.此外，该文还提出了随机敏感性分析方法来研究噪声对捕食者-食饵种群动力学的影响.研究结果表明，较小强度的噪声可以抑制种群规模的扩大，而较大强度的噪声则会导致种群的灭绝.

关键词: 捕食者-食饵相互作用, 随机模型, 随机敏感性分析, 遍历性, 平稳分布

Abstract:

Predator-prey interactions serve a pivotal role in protecting species diversity. In this study, the parameter $λ$ is presented to show the stochastic dynamics of a predator-prey model. The results show that the predator population tends to become extinct if $λ$ < 0. Furthermore, the solution of the prey population converges weakly to an invariant probability distribution. If $λ$>0, we find that the stochastic system admits a unique ergodic stationary distribution. In addition, stochastic sensitivity analysis is proposed to study the effects of noise on the dynamics of predator-prey populations. Our findings suggest that small-intensity noise can suppress population size enlargement, while large-intensity noise can lead to the extinction of populations.

Key words: Predator-prey interaction, Stochastic model, Stochastic sensitivity analysis, Ergodic property, Stationary distribution

中图分类号:

O175

王腾飞,冯涛,孟新柱. 具有Crowley-Martin型功能反应的捕食者-食饵模型的复杂动力学和随机敏感性分析[J]. 数学物理学报, 2021, 41(4): 1192-1203.

Tengfei Wang,Tao Feng,Xinzhu Meng. Complex Dynamics and Stochastic Sensitivity Analysis of a Predator-Prey Model with Crowley-Martin Type Functional Response[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1192-1203.

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