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Discontinuity, Nonlinearity, and Complexity 7(4) (2018) 413--427 | DOI:10.5890/DNC.2018.12.006

I. El Harraki, R. Yafia, A. Boutoulout, M. A. Aziz-Alaoui

Ecole Nationale Sup´erieure des Mines de Rabat, Morocco

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Abstract

In this paper, we study the effect of harvesting on the qualitative properties of predator-prey model with modified Leslie-Gower and Holling Type II functional responses. The model is given by a system of two ordinary differential equations with non-selective constants harvesting terms. We investigate the impact of harvesting terms on the boundedness of solutions, on the existence of the attraction set, on the stability of different equilibrium points. A Lyapunov function is used to prove the global stability of the interior equilibrium. We also, discussed the policy of optimal harvest and we got the solution for the interior equilibriumby the Pontryaginmaximum criterion. Finally, our theoretical results are illustrated by a numerical simulations.

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