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Open AccessArticle

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

1
College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, China
2
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 173; https://doi.org/10.3390/math8020173
Received: 19 December 2019 / Revised: 19 January 2020 / Accepted: 21 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Applied Analysis of Ordinary Differential Equations 2020)
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.
Keywords: permanence; extinction; phytoplankton; feedback controls permanence; extinction; phytoplankton; feedback controls
MDPI and ACS Style

Zhao, L.; Chen, F.; Song, S.; Xuan, G. The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls. Mathematics 2020, 8, 173.

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