CONDITIONS FOR PERMANENCE AND ERGODICITY OF CERTAIN STOCHASTIC PREDATOR-PREY MODELS

被引：125

作者：

Nguyen Huu Du ^{[1
]}

Dang Hai Nguyen ^{[2
]}

Yin, G. George ^{[2
]}

机构：

[1] Hanoi Natl Univ, Dept Math Mech & Informat, 334 Nguyen Trai, Hanoi, Vietnam

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2016年 / 53卷 / 01期

基金：

美国国家科学基金会;

关键词：

Ergodicity; extinction; permanence; predator-prey; Beddington-DeAngelis functional response; stationary distribution; DEGENERATE ELLIPTIC-OPERATORS; LOTKA-VOLTERRA MODEL; CLASSIFICATION; BEHAVIOR;

D O I：

10.1017/jpr.2015.18

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we derive sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with a Beddington-DeAngelis functional response. The conditions obtained are in fact very close to the necessary conditions. Both nondegenerate and degenerate diffusions are considered. One of the distinctive features of our results is that they enable the characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to the existing literature and matters related to other stochastic predator-prey models are also given.

引用

页码：187 / 202

页数：16

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