A two non-linear dynamic models, first one in two state variables and one control and the second one with three state variables and one control, are presented for the purpose of finding the optimal combination of exploitation, capital investment and price variation in the commercial fishing industry. This optimal combination is determined in terms of management policies. Exploitation, capital and price variation are controlled through the utilization rate of available capital. A novel feature in this model is that the variation (...) of the capital depends on the income. (shrink)

We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when (...) the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability. (shrink)

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is (...) assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities. (shrink)

This work presents a stock/effort model describing both harvested fish population and fishing effort dynamics. The fishing effort dynamic is controlled by investment which corresponds to the revenue proportion generated by the activity. The dynamics are subject to a set of economic and biological state constraints. The analytical study focuses on the compatibility between state constraints and controlled dynamics. By using the mathematical concept of viability kernel, we reveal situations and management options that guarantee a sustainable system.

Abstract This work is about the viability domain corresponding to a model of fisheries management. The dynamic is subject of two constraints. The biological constraint ensures the stock perennity where as the economic one ensures a minimum income for the fleets. Using the mathematical concept of viability kernel, we find out a viability domain which simultaneously enables the fleets to exploit the resource, to ensure a minimum income and stock perennity. Content Type Journal Article Category Regular Article Pages 1-19 DOI (...) 10.1007/s10441-012-9153-5 Authors C. Sanogo, LIRNE, Mathmatics Engineering Team, Ibn Tofail University, Kenitra, Morocco S. Ben Miled, ENIT-LAMSIN, Tunis el Manar University, Tunis, Tunisia N. Raissi, LAA, Mohamed V University, Rabat, Morocco Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)