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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


The Effect of non-Selective Harvesting in Predator-Prey Model with Modified Leslie-Gower and Holling Type II Schemes

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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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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