Gompertzian law of growth for reserved area fishery model with non-selective harvesting in unreserved area

Abstract

This paper deals with the combined harvesting of two species from a prey-predator fishery model in an unreserved area of a marine aquatic eco-system where in primary phase of life the prey species is in marine protected areas (reserved areas). In a reserved area no harvesting and no predation can occur So prey species can grow smoothly and after that they migrate to unreserved open access areas where harvesting and predation are permitted. These kinds of fisheries are a good process to maintain the prey-predator biomass level up to a good size in the long run. They can also prevent species extinction. Here the prey follows the Gompertz law of growth in both reserved and unreserved areas. Initially the dynamic behaviour of the system was studied under a deterministic case with local stability and bionomic equilibrium. The optimal harvesting policy is studied using Pontryagian’s maximum principle. In second part of the work, we investigated the stability of the model under stochastic arena using Gaussian white noise. Finally, a comparison has been made. Moreover, the model has also been discussed through numerical example.