Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls

Author:

Zhao Liang12ORCID,Qin Bin2,Chen Fengde3

Affiliation:

1. School of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, China

2. College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, China

3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350116, China

Abstract

A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

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