Periodic Oscillations in a Chemostat Model with Two Discrete Delays

Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the...

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Main Authors: Tiansi Zhang, Xuehui Ji, Bo Li
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/306302
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author Tiansi Zhang
Xuehui Ji
Bo Li
author_facet Tiansi Zhang
Xuehui Ji
Bo Li
author_sort Tiansi Zhang
collection DOAJ
description Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results.
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institution Kabale University
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publishDate 2015-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-83adcd0a2a304c238eda85f1ecb1d6552025-08-20T03:37:11ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/306302306302Periodic Oscillations in a Chemostat Model with Two Discrete DelaysTiansi Zhang0Xuehui Ji1Bo Li2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaPeriodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results.http://dx.doi.org/10.1155/2015/306302
spellingShingle Tiansi Zhang
Xuehui Ji
Bo Li
Periodic Oscillations in a Chemostat Model with Two Discrete Delays
Discrete Dynamics in Nature and Society
title Periodic Oscillations in a Chemostat Model with Two Discrete Delays
title_full Periodic Oscillations in a Chemostat Model with Two Discrete Delays
title_fullStr Periodic Oscillations in a Chemostat Model with Two Discrete Delays
title_full_unstemmed Periodic Oscillations in a Chemostat Model with Two Discrete Delays
title_short Periodic Oscillations in a Chemostat Model with Two Discrete Delays
title_sort periodic oscillations in a chemostat model with two discrete delays
url http://dx.doi.org/10.1155/2015/306302
work_keys_str_mv AT tiansizhang periodicoscillationsinachemostatmodelwithtwodiscretedelays
AT xuehuiji periodicoscillationsinachemostatmodelwithtwodiscretedelays
AT boli periodicoscillationsinachemostatmodelwithtwodiscretedelays