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

Liang Zhao, Fengde Chen, Saixi Song and Guizhen Xuan
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Liang Zhao: College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, China
Fengde Chen: College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, China
Saixi Song: College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, China
Guizhen Xuan: College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, Guangxi, China

Mathematics, 2020, vol. 8, issue 2, 1-13

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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