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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2020

04-02-2020 | Original Research

Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting

Authors: Xin-You Meng, Yu-Qian Wu

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2020

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Abstract

In this paper, a singular phytoplankton–zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy number. By using the utility function method, the transformed differential equation is reduced to a differential equation. In absence of economic profit, the existence of positive equilibria, local stability and global stability for the interior equilibrium of the present differential system are discussed, the conditions of Hopf bifurcation occurring at the positive equilibrium are given, and the corresponding nonlinear feedback controller is designed to eliminate Hopf bifurcation. In presence of economic profit, the corresponding differential algebraic model is proposed and some conditions of the existence of the interior equilibrium are derived. By regarding economic profit as bifurcation parameter, singular induced bifurcation occurring is investigated, and a linear controller is designed to remove such bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal harvesting policy to maximize the benefit as well as conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical results after each part. Results show that imprecise parameters not only affect the interior equilibrium and the bionomic equilibrium of system, but also affect the critical value of bifurcation and branch range.
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Metadata
Title
Dynamical analysis of a fuzzy phytoplankton–zooplankton model with refuge, fishery protection and harvesting
Authors
Xin-You Meng
Yu-Qian Wu
Publication date
04-02-2020
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2020
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01321-y

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