Effect of a Toxicant on the Dynamics of a Spatial Fishery

Abstract

In this paper, we present a mathematical model of a spatial fishery with two patches. The first patch is unpolluted while fishes are infected by some toxicants released by industrial wastes in the other one. The fish stock can move between these zones, on which they are harvested by fishing fleets. Fish movements between the zones, as well as vessels displacements, are assumed to take place at a faster time scale than the variation of the fish stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and fishing effort. This reduced model is analyzed and we look for existence of limit cycle. We also present numerical simulations to illustrate the results.