Persistence and extinction for a stochastic logistic model with infinite delay

This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our res...

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Main Authors:	Chun Lu, Xiaohua Ding
Format:	Article
Language:	English
Published:	Texas State University 2013-11-01
Series:	Electronic Journal of Differential Equations
Subjects:	White noise persistence extinction delay
Online Access:	http://ejde.math.txstate.edu/Volumes/2013/262/abstr.html

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record_format	Article
spelling	doaj-6c8ce28a189b479cb25e3174110017182020-11-24T23:43:28ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-11-012013262,116Persistence and extinction for a stochastic logistic model with infinite delayChun Lu0Xiaohua Ding1 Harbin Institute of Technology, Weihai, China Harbin Institute of Technology, Weihai, China This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and extinction for the stochastic model in the autonomous case. Numerical simulations illustrate the theoretical results.http://ejde.math.txstate.edu/Volumes/2013/262/abstr.htmlWhite noisepersistenceextinctiondelay
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Chun Lu Xiaohua Ding
spellingShingle	Chun Lu Xiaohua Ding Persistence and extinction for a stochastic logistic model with infinite delay Electronic Journal of Differential Equations White noise persistence extinction delay
author_facet	Chun Lu Xiaohua Ding
author_sort	Chun Lu
title	Persistence and extinction for a stochastic logistic model with infinite delay
title_short	Persistence and extinction for a stochastic logistic model with infinite delay
title_full	Persistence and extinction for a stochastic logistic model with infinite delay
title_fullStr	Persistence and extinction for a stochastic logistic model with infinite delay
title_full_unstemmed	Persistence and extinction for a stochastic logistic model with infinite delay
title_sort	persistence and extinction for a stochastic logistic model with infinite delay
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2013-11-01
description	This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and extinction for the stochastic model in the autonomous case. Numerical simulations illustrate the theoretical results.
topic	White noise persistence extinction delay
url	http://ejde.math.txstate.edu/Volumes/2013/262/abstr.html
work_keys_str_mv	AT chunlu persistenceandextinctionforastochasticlogisticmodelwithinfinitedelay AT xiaohuading persistenceandextinctionforastochasticlogisticmodelwithinfinitedelay
_version_	1725501502683873280

Persistence and extinction for a stochastic logistic model with infinite delay

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