The periodic solutions of a stochastic chemostat model with periodic washout rate

Liang Wang; Daqing Jiang; Donal O'Regan

doi:10.1016/j.cnsns.2016.01.002

The periodic solutions of a stochastic chemostat model with periodic washout rate

Liang Wang
, Daqing Jiang
, Donal O'Regan

Mathematics

Northeast Normal University
Faculty of Sciences, King Abdulaziz University
China University of Petroleum (East China)

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

43 Citations (Scopus)

Abstract

A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii's theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally attractive. Numerical simulations are carried out to illustrate our main conclusions.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	37
DOIs	https://doi.org/10.1016/j.cnsns.2016.01.002
Publication status	Published - 1 Aug 2016

Keywords

Chemostat model
Globally attractive
Monod response function
Periodic Markov process
Periodic solution
Periodic washout rate

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10.1016/j.cnsns.2016.01.002

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title = "The periodic solutions of a stochastic chemostat model with periodic washout rate",

abstract = "A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii's theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally attractive. Numerical simulations are carried out to illustrate our main conclusions.",

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AU - Jiang, Daqing

AU - O'Regan, Donal

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Y1 - 2016/8/1

N2 - A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii's theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally attractive. Numerical simulations are carried out to illustrate our main conclusions.

AB - A stochastic chemostat model with periodic washout rate is proposed in this paper. First, sufficient conditions are established for the existence of stochastic nontrivial positive periodic solution for the system, on the basis of Khasminskii's theory for periodic Markov processes. Furthermore, we observe that there exists a unique boundary periodic solution of the stochastic model which is globally attractive. Numerical simulations are carried out to illustrate our main conclusions.

KW - Chemostat model

KW - Globally attractive

KW - Monod response function

KW - Periodic Markov process

KW - Periodic solution

KW - Periodic washout rate

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

The periodic solutions of a stochastic chemostat model with periodic washout rate

Abstract

Keywords

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