Effect of a nonlinear demand function on the dynamics of a fishery

Abstract

In this work, we present and analyze a fishery model with a price variation. We take into account the evolution in time of the fish biomass and the harvesting effort, while the price of fish is dependent on supply and demand. Assuming that the price variation occurs at a fast time scale. We assume that the stock and the effort evolution follow a slow time scale. Considering the different time scales, the model is reduced to a 2D model. We analyze the obtained model, and depending on the value of a parameter, there are two main cases that can arise: a fish exclusion case and a sustainable fishery. To avoid Fish Extinction we introduce a control parameter and we study the impact of the number of sites on the catch that allow the undesirable case to be avoided.