The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls

A non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one o...

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Main Authors:	Liang Zhao, Fengde Chen, Saixi Song, Guizhen Xuan
Format:	Article
Language:	English
Published:	MDPI AG 2020-02-01
Series:	Mathematics
Subjects:	permanence extinction phytoplankton feedback controls
Online Access:	https://www.mdpi.com/2227-7390/8/2/173

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spelling	doaj-a1b3367d3c0a4249bc32c4fb367687532020-11-25T02:05:26ZengMDPI AGMathematics2227-73902020-02-018217310.3390/math8020173math8020173The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback ControlsLiang Zhao0Fengde Chen1Saixi Song2Guizhen Xuan3College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, ChinaCollege of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, ChinaA non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one of the species by using some suitable Lyapunov type extinction function. Our analyses extend those of Xie et al. (Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton. Advances in Difference Equations, 2016, 2016, 258) and show that the feedback controls and toxic substances have no effect on the permanence of the system but play a crucial role on the extinction of the system. Some known results are extended.https://www.mdpi.com/2227-7390/8/2/173permanenceextinctionphytoplanktonfeedback controls
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Liang Zhao Fengde Chen Saixi Song Guizhen Xuan
spellingShingle	Liang Zhao Fengde Chen Saixi Song Guizhen Xuan The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls Mathematics permanence extinction phytoplankton feedback controls
author_facet	Liang Zhao Fengde Chen Saixi Song Guizhen Xuan
author_sort	Liang Zhao
title	The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls
title_short	The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls
title_full	The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls
title_fullStr	The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls
title_full_unstemmed	The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls
title_sort	extinction of a non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-02-01
description	A non-autonomous allelopathic phytoplankton model with nonlinear inter-inhibition terms and feedback controls is studied in this paper. Based on the comparison theorem of differential equation, some sufficient conditions for the permanence of the system are obtained. We study the extinction of one of the species by using some suitable Lyapunov type extinction function. Our analyses extend those of Xie et al. (Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton. Advances in Difference Equations, 2016, 2016, 258) and show that the feedback controls and toxic substances have no effect on the permanence of the system but play a crucial role on the extinction of the system. Some known results are extended.
topic	permanence extinction phytoplankton feedback controls
url	https://www.mdpi.com/2227-7390/8/2/173
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The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls

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