Stationary distribution and extinction of a stochastic predator-prey model with additional food and nonlinear perturbation

被引：56

作者：

Liu, Qun ^{[1
,2
]}

Jiang, Daqing ^{[1
,3
,4
]}

Hayat, Tasawar ^{[3
,5
]}

Ahmad, Bashir ^{[3
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat MOE, Changchun 130024, Jilin, Peoples R China

[2] Yulin Normal Univ, Sch Math & Stat, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Guangxi, Peoples R China

[3] King Abdulaziz Univ, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah, Saudi Arabia

[4] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[5] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 320卷

关键词：

Stochastic predator-prey model; Stationary distribution and ergodicity; Extinction; Habitat complexity; Additional food; Nonlinear perturbation; HABITAT COMPLEXITY; DIDINIUM-NASUTUM; WEB STABILITY; TIME-DELAY; DYNAMICS; SIZE; SYSTEM; GROWTH;

D O I：

10.1016/j.amc.2017.09.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we formulate and analyze a stochastic predator-prey model with additional food and nonlinear perturbation. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution of the positive solution to the model. Then we obtain sufficient conditions for extinction of the predator species in two cases, one is the prey species surviving and the predator species extinction; the other is both the prey and predator species are extinct. Finally, some examples together with numerical simulations are provided to illustrate the analytical results. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：226 / 239

页数：14

共 50 条

[1] Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation
Zu, Li
Jiang, Daqing
Jiang, Fuquan
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[2] Stationary distribution and extinction of a stochastic predator-prey model with distributed delay
Liu, Qun
Jiang, Daqing
[J]. APPLIED MATHEMATICS LETTERS, 2018, 78 : 79 - 87
[3] Stationary distribution and extinction of a stochastic predator-prey model with herd behavior
Liu, Qun
Jiang, Daqing
Hayat, Tasawar
Alsaedi, Ahmed
[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2018, 355 (16): : 8177 - 8193
[4] Extinction and stationary distribution of stochastic predator-prey model with group defense behavior
Pei, Yansong
Liu, Bing
Qi, Haokun
[J]. MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2022, 19 (12) : 13062 - 13078
[5] Stationary distribution of a stochastic reaction-diffusion predator-prey model with additional food and fear effect
Qi, Haokun
Liu, Bing
[J]. APPLIED MATHEMATICS LETTERS, 2024, 150
[6] Stationary distribution of a stochastic predator-prey model with hunting cooperation
Qi, Haokun
Meng, Xinzhu
Hayat, Tasawar
Hobiny, Aatef
[J]. APPLIED MATHEMATICS LETTERS, 2022, 124
[7] EXTINCTION AND STATIONARY DISTRIBUTION OF A STOCHASTIC PREDATOR-PREY MODEL WITH HOLLING II FUNCTIONAL RESPONSE AND STAGE STRUCTURE OF PREY
Wang, Rongyan
Zhao, Wencai
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2022, 12 (01): : 50 - 68
[8] Extinction and ergodic stationary distribution of a Markovian-switching prey-predator model with additional food for predator
Guo, Xiaoxia
Ruan, Dehan
[J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2020, 15
[9] Stationary distribution and periodic solution for stochastic predator-prey systems with nonlinear predator harvesting
Zuo, Wenjie
Jiang, Daqing
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 36 : 65 - 80
[10] STATIONARY DISTRIBUTION AND PERSISTENCE OF A STOCHASTIC PREDATOR-PREY MODEL WITH A FUNCTIONAL RESPONSE
Lv, Jingliang
Liu, Heng
Zou, Xiaoling
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (01): : 1 - 11

← 1 2 3 4 5 →