A model of a fishery with fish stock involving delay equations-Reference-Cited by-同舟云学术

A model of a fishery with fish stock involving delay equations

Published:2009-12-13 Issue:1908 Volume:367 Page:4907-4922
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Auger P.¹,Ducrot Arnaud²

Affiliation:

1. UMI IRD 209 UMMISCO Centre IRD de l’île de France, 32 Avenue Henri Varagnat, 93143 Bondy cedex, France

2. UMR CNRS 5251 IMB & INRIA sud-ouest Anubis, Université of Bordeaux, 146 rue Léo Saignat, 33076 Bordeaux, France

Abstract

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2009.0147

Reference19 articles.

1. Local existence or a class of partial neutral functional differential equations with infinite delay;Adimy M.;Diff. Equ. Dyn. Syst.,2004

2. Existence and stability for some partial neutral functional differential equations with infinite delay

3. Adimy M. Alia M.& Ezzinbi K. Submitted. Partial neutral functional differential equations with infinite delay in extrapolation spaces.

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