Existence and persistence of positive solution for a stochastic turbidostat model

Existence and persistence of positive solution for a stochastic turbidostat model

Abstract A novel stochastic turbidostat model is investigated in this paper. The stochasticity in the model comes from the maximal growth rate influenced by white noise. Firstly, the existence and uniqueness of the positive solution for the system are demonstrated. Secondly, we analyze the persisten...

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Main Authors: Zuxiong Li, Yu Mu, Huili Xiang, Hailing Wang
Format: Article
Language:English
Published: SpringerOpen 2017-12-01
Series:Advances in Difference Equations
Subjects:
turbidostat model
white noise
persistence in mean
stochastic persistence
extinction
Online Access:http://link.springer.com/article/10.1186/s13662-017-1448-z
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spelling doaj-a3470a3fb7c6423fb726e019c9270ff82020-11-25T02:49:24ZengSpringerOpenAdvances in Difference Equations1687-18472017-12-012017111710.1186/s13662-017-1448-zExistence and persistence of positive solution for a stochastic turbidostat modelZuxiong Li0Yu Mu1Huili Xiang2Hailing Wang3Department of Mathematics, Hubei University for NationalitiesDepartment of Mathematics, Hubei University for NationalitiesDepartment of Mathematics, Hubei University for NationalitiesDepartment of Mathematics, Hubei University for NationalitiesAbstract A novel stochastic turbidostat model is investigated in this paper. The stochasticity in the model comes from the maximal growth rate influenced by white noise. Firstly, the existence and uniqueness of the positive solution for the system are demonstrated. Secondly, we analyze the persistence in mean and stochastic persistence of the system, respectively. Sufficient conditions about the extinction of the microorganism are obtained. Finally, numerical simulation results are given to support the theoretical conclusions.http://link.springer.com/article/10.1186/s13662-017-1448-zturbidostat modelwhite noisepersistence in meanstochastic persistenceextinction
collection DOAJ
language English
format Article
sources DOAJ
author Zuxiong Li
Yu Mu
Huili Xiang
Hailing Wang
spellingShingle Zuxiong Li
Yu Mu
Huili Xiang
Hailing Wang
Existence and persistence of positive solution for a stochastic turbidostat model
Advances in Difference Equations
turbidostat model
white noise
persistence in mean
stochastic persistence
extinction
author_facet Zuxiong Li
Yu Mu
Huili Xiang
Hailing Wang
author_sort Zuxiong Li
title Existence and persistence of positive solution for a stochastic turbidostat model
title_short Existence and persistence of positive solution for a stochastic turbidostat model
title_full Existence and persistence of positive solution for a stochastic turbidostat model
title_fullStr Existence and persistence of positive solution for a stochastic turbidostat model
title_full_unstemmed Existence and persistence of positive solution for a stochastic turbidostat model
title_sort existence and persistence of positive solution for a stochastic turbidostat model
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2017-12-01
description Abstract A novel stochastic turbidostat model is investigated in this paper. The stochasticity in the model comes from the maximal growth rate influenced by white noise. Firstly, the existence and uniqueness of the positive solution for the system are demonstrated. Secondly, we analyze the persistence in mean and stochastic persistence of the system, respectively. Sufficient conditions about the extinction of the microorganism are obtained. Finally, numerical simulation results are given to support the theoretical conclusions.
topic turbidostat model
white noise
persistence in mean
stochastic persistence
extinction
url http://link.springer.com/article/10.1186/s13662-017-1448-z
work_keys_str_mv AT zuxiongli existenceandpersistenceofpositivesolutionforastochasticturbidostatmodel
AT yumu existenceandpersistenceofpositivesolutionforastochasticturbidostatmodel
AT huilixiang existenceandpersistenceofpositivesolutionforastochasticturbidostatmodel
AT hailingwang existenceandpersistenceofpositivesolutionforastochasticturbidostatmodel
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