Permanence and periodic solution for a modified Leslie-Gower type predator-prey model with diffusion and non constant coefficients

Moussaoui Ali, M. A. Aziz Alaoui, R. Yafia


In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results.


Population dynamics, prey-predator model, permanence

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 ISSN: 1314-684X (print), 1314-7218 (online)