Article ID Journal Published Year Pages File Type
840382 Nonlinear Analysis: Theory, Methods & Applications 2013 16 Pages PDF
Abstract

The present paper aims to provide a detailed qualitative analysis of a non-smooth Gause predator–prey model. In this model, the saturating functional response function with a discontinuity at a critical prey density was employed to show the effects of a prey refuge on the population dynamic behavior. Analysis of this model revealed rich dynamics including locally (or globally) stable canard cycles, a locally (globally) stable pseudo-equilibrium, unbounded trajectories in which both populations go to infinity or the prey goes to infinity and the predator dies out eventually. The main purpose of the present work is to carry out a completely qualitative analysis for this model. In particular, two sets of sufficient conditions drive both populations to approach infinity and the sufficient and necessary conditions for all of the other main results are presented.

Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
Authors
, ,