文章基本信息

标题：Dynamic behaviors of a turbidostat model with Tissiet functional response and discrete delay
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作者：Yong Yao ; Zuxiong Li ; Huili Xiang 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：106
DOI：10.1186/s13662-018-1566-2
语种：English
出版社：Hindawi Publishing Corporation
摘要：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.
关键词：Turbidostat ; Time delay ; Hopf bifurcation ; Stability permanence