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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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  • 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)

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.

Suggested Citation

  • Liang Zhao & Fengde Chen & Saixi Song & Guizhen Xuan, 2020. "The Extinction of a Non-Autonomous Allelopathic Phytoplankton Model with Nonlinear Inter-Inhibition Terms and Feedback Controls," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:173-:d:315404
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    References listed on IDEAS

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    1. Qinglong Wang & Zhijun Liu, 2013. "Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, May.
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