Dynamical Study of Quadrating harvesting of prey in a Predator-Prey Model following Modified Leslie-Gower type Predation and Crowley-Martin type Functional Response

  • Manpreet Kaur, Reenu Rani, Rachna Bhatia, G. N. Verma

Abstract

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.

Published
2019-11-27
How to Cite
Rachna Bhatia, G. N. Verma, M. K. R. R. (2019). Dynamical Study of Quadrating harvesting of prey in a Predator-Prey Model following Modified Leslie-Gower type Predation and Crowley-Martin type Functional Response. International Journal of Control and Automation, 12(5), 699-709. Retrieved from https://sersc.org/journals/index.php/IJCA/article/view/5757
Section
Articles