%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Auger, Pierre
%A Ducrot, A.
%T A model of a fishery with fish stock involving delay equations
%D 2009
%L fdi:010048381
%G ENG
%J Philosophical Transactions of the Royal Society a - Mathematical Physical and Engineering Sciences
%@ 1364-503X
%K fishery models ; delay differential equation ; Hopf bifurcation
%M ISI:000271332700014
%N 1908
%P 4907-4922
%R 10.1098/rsta.2009.0147
%U https://www.documentation.ird.fr/hor/fdi:010048381
%> https://www.documentation.ird.fr/intranet/publi/2009/11/010048381.pdf
%V 367
%W Horizon (IRD)
%X 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.
%$ 020 ; 040