Dynamical Study of Quadrating harvesting of prey in a Predator-Prey Model following Modiﬁed Leslie-Gower type Predation and Crowley-Martin type Functional Response
In the present article, the local dynamics of a predator-prey system incorporating quadrating harvesting for prey is proposed and examined. The Crowley-Martin functional response is considered in the system whereas predator is supposedtobeofModiﬁedLeslie-Gowertype. Themodelisgovernedbysetoftwoordinarydiﬀerentialequations. It hasbeeninvestigatedthatallthepossiblesolutionsoftheproposedmodelarealwayspositiveandboundeduniformly. The possible steady states of the model are obtained under some conditions where the system exhibits at most two non-zero positive interior steady states under certain conditions. The dynamics of all these positive steady states are investigated using Routh-Hurwitz Criteria. Optimal harvesting policy is investigated using Pontryagin’s Maximum Principle to prevent the biological species from extinction and to preserve a sustainable ﬁshery system. To exemplify the analytical results, some numerical simulations are also executed for suitable choice of parameters.