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

Abstract

Abstract-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.

Positive almost periodic solutions of nonautonomous evolution equations and application to Lotka–Volterra systems

“…Finally, an illustrating application to the Lotka–Volterra predator–prey model () in a bounded domain (the habitat) $$$ \Omega \subset {\mathbb{R}}^N $$$ (for $$$ N\ge 1 $$$) with Lipschitz type boundary $$$ \mathrm{\partial \Omega } $$$ and time–dependent parameters in a generalized almost periodic environment is provided. For more details about the study of models of type () involving almost periodic parameters, we refer to previous works [7–10] and references therein.…”

Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses

“…For this reason, Aziz-Alaoui [2] modified the logistic form and proposed the Leslie-Gower-type functional response hx/(a + y), where a is a positive constant and measures the environmental protection for predator. With such a functional response, Aziz-Alaoui et al studied some predator-prey models in spatially homogeneous or inhomogeneous cases; see [7,[15][16][17]25]. Based on and motivated by all the above-mentioned, in this paper, we introduce the following nondimensional reactionhttp://www.journals.vu.lt/nonlinear-analysis diffusion system…”