| Abstrakt: |
In this work, we present a mathematical fishery model, which is a set of five ordinary differential equations governing the fish stock. The first two ODEs correspond to the evolution of two populations moving and growing between two areas, and exploited by two fishing fleets represented by their fishing efforts. The evolution of the fishing efforts are represented by two other ODEs. The catch function is assumed to be non-linear with a price variation. The evolution of the price with respect to time is represented in the fifth equation by the difference between supply (which is the catch, in our case) and demand (which corresponds to a non-linear demand function). We suppose that the growth of fish and the evolution of fishing efforts follow a slow time scale, while the fish migration, the vessels movement, and the price variation occur at a fast time scale. Then, we use an aggregation of variables method to obtain what we call "a reduced model". The aggregated fishery model is analyzed mathematically, which shows that two main cases can occur under some conditions: A fish extinction case and a sustainable one. Finally, we prove that we can switch from an undesirable case to a desirable one by controlling the catch part in the model. Some numerical simulations are also given in this work. [ABSTRACT FROM AUTHOR] |
