Effort Dynamics in a Selective Harvesting Prey-Predator Fishery with Beddington- DeAngelis Functional Response

In this paper, regulation of selective harvesting of a prey-predator fishery with Beddington-DeAngelis functional response [1,2] is discussed, considering taxation as a control instrument and harvesting effort as a dynamic variable. The Beddington-DeAngelis functional response is similar to the Holling type II [3] functional response but contains one extra term describing mutual interference by the predator. In this paper we assume that fishing is permitted only for the predator fish species after imposing a tax per unit harvested biomass by the regulatory agencies in order to control over exploitation. Considering the effort as the dynamic variable i.e. time dependent variable, the non-trivial interior equilibrium point is determined and the local and global stability of this equilibrium point is discussed. The results are illustrated with the help of a numerical example.