A model of a fishery with fish stock involving delay equations.
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.
Auger
P
P
UMI IRD 209 UMMISCO Centre IRD de l'île de France, 32 Avenue Henri Varagnat, 93143 Bondy cedex, France.
Ducrot
Arnaud
A
D000818:Animals; D003198:Computer Simulation; D005398:Fisheries / Q000191:economics / Q000379:methods*; D005399:Fishes / Q000254:growth & development*; D008954:Models, Biological; D018803:Models, Economic