Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation

We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which imp...

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Main Authors: Haihong Li, Daqing Jiang, Fuzhong Cong, Haixia Li
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/720283
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author Haihong Li
Daqing Jiang
Fuzhong Cong
Haixia Li
author_facet Haihong Li
Daqing Jiang
Fuzhong Cong
Haixia Li
author_sort Haihong Li
collection DOAJ
description We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.
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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-04447c99c7e645728d8ffe46d31be19c2025-02-03T01:22:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/720283720283Persistence and Nonpersistence of a Predator Prey System with Stochastic PerturbationHaihong Li0Daqing Jiang1Fuzhong Cong2Haixia Li3College of Science, China University of Petroleum (East China), Qingdao 266580, ChinaCollege of Science, China University of Petroleum (East China), Qingdao 266580, ChinaDepartment of Basic Courses, Air Force Aviation University, Changchun, Jilin 130022, ChinaSchool of Business, Northeast Normal University, Changchun, Jilin 130024, ChinaWe analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.http://dx.doi.org/10.1155/2014/720283
spellingShingle Haihong Li
Daqing Jiang
Fuzhong Cong
Haixia Li
Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
Abstract and Applied Analysis
title Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
title_full Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
title_fullStr Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
title_full_unstemmed Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
title_short Persistence and Nonpersistence of a Predator Prey System with Stochastic Perturbation
title_sort persistence and nonpersistence of a predator prey system with stochastic perturbation
url http://dx.doi.org/10.1155/2014/720283
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AT daqingjiang persistenceandnonpersistenceofapredatorpreysystemwithstochasticperturbation
AT fuzhongcong persistenceandnonpersistenceofapredatorpreysystemwithstochasticperturbation
AT haixiali persistenceandnonpersistenceofapredatorpreysystemwithstochasticperturbation