Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay

Abstract In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic stability of its equilibria and the phenomenon of Hopf bifurcation for this syste...

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Main Authors:	Yong Yao, Zuxiong Li, Huili Xiang, Hailing Wang
Format:	Article
Language:	English
Published:	SpringerOpen 2018-03-01
Series:	Advances in Difference Equations
Subjects:	Turbidostat Time delay Hopf bifurcation Stability permanence
Online Access:	http://link.springer.com/article/10.1186/s13662-018-1566-2

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spelling	doaj-ab2a630064834c118f19950725c4f00d2020-11-25T00:36:29ZengSpringerOpenAdvances in Difference Equations1687-18472018-03-012018111510.1186/s13662-018-1566-2Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delayYong Yao0Zuxiong Li1Huili 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 In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic stability of its equilibria and the phenomenon of Hopf bifurcation for this system are considered. Using the Liapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Furthermore, based on some knowledge of limit set, we show the necessary and sufficient conditions of permanent of the turbidostat model. Finally, numerical simulations are offered to support our results.http://link.springer.com/article/10.1186/s13662-018-1566-2TurbidostatTime delayHopf bifurcationStability permanence
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yong Yao Zuxiong Li Huili Xiang Hailing Wang
spellingShingle	Yong Yao Zuxiong Li Huili Xiang Hailing Wang Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay Advances in Difference Equations Turbidostat Time delay Hopf bifurcation Stability permanence
author_facet	Yong Yao Zuxiong Li Huili Xiang Hailing Wang
author_sort	Yong Yao
title	Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
title_short	Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
title_full	Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
title_fullStr	Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
title_full_unstemmed	Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
title_sort	dynamic behaviors of a turbidostat model with tissiet functional response and discrete delay
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2018-03-01
description	Abstract In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic stability of its equilibria and the phenomenon of Hopf bifurcation for this system are considered. Using the Liapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Furthermore, based on some knowledge of limit set, we show the necessary and sufficient conditions of permanent of the turbidostat model. Finally, numerical simulations are offered to support our results.
topic	Turbidostat Time delay Hopf bifurcation Stability permanence
url	http://link.springer.com/article/10.1186/s13662-018-1566-2
work_keys_str_mv	AT yongyao dynamicbehaviorsofaturbidostatmodelwithtissietfunctionalresponseanddiscretedelay AT zuxiongli dynamicbehaviorsofaturbidostatmodelwithtissietfunctionalresponseanddiscretedelay AT huilixiang dynamicbehaviorsofaturbidostatmodelwithtissietfunctionalresponseanddiscretedelay AT hailingwang dynamicbehaviorsofaturbidostatmodelwithtissietfunctionalresponseanddiscretedelay
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Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay

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