Sustainable harvesting policies for a fishery model including spawning periods and taxation

Abstract

We consider a fishery model containing predator fish and prey fish in which the predators are the commercial fish. We also divide each year into a spawning period and a harvesting period. The modified Lotka-Volterra interspecific competition model is applied to the fisheries system in spawning periods while an additional variable, harvesting effort of fishermen, is introduced to the system during the harvesting period. The existence of steady state solutions and closed orbits are theoretically studied and the local and global stabilities of steady state solutions are also studied. The fisheries population dynamics, total revenue earned by government and fishermen are investigated numerically for a range of taxation levels and a range of limits imposed on maximum fishing effort.