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

Abstract

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

CLC Number:

O175

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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Figures/Tables 5

References 42

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符号	生物学意义
$a$	在没有捕食的情况下, 食饵种群的内在增长率
$b$	攻击系数
$\alpha$	处理时间
$\beta$	捕食者个体之间的干扰程度
$c$	在没有捕食的情况下, 捕食者种群的内在增长率
$f$	捕食的转化率
$\sigma_i^2$	布朗运动$B_i$的强度$(i = 1, 2)$

[1]	Guijie Lan,Yingjie Fu,Chunjin Wei,Shuwen Zhang. Stationary Distribution and Periodic Solution for Stochastic Predator-Prey Systems with Holling-Type Ⅲ Functional Response [J]. Acta mathematica scientia,Series A, 2018, 38(5): 984-1000.
[2]	Wei Fengying, Lin Qingteng. Extinction and Distribution for an SIQS Epidemic Model with Quarantined-Adjusted Incidence [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1148-1161.
[3]	Tang Yourong, Liu Zaiming, Hou Zhenting. The Ergodic Property and Equilibrium Distribution of the Generalized Birth and Death Processes [J]. Acta mathematica scientia,Series A, 1998, 18(1): 25-32.

Complex Dynamics and Stochastic Sensitivity Analysis of a Predator-Prey Model with Crowley-Martin Type Functional Response

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