Effects of Nonlinear Growth and Death Rates for the Predator in Predator-Prey Type Models

Abstract

Following a recent paper by Terry [1] and a recent work of the two authors [2], in the present work we study the effects of nonlinear (w.r.t. the functional response) growth and death ratesfor the predator by comparing models incorporating such rates with the classical models with a linear growth rateand a constant death rate. We study a three-dimensional ODE system modelling the interactions between a predator population andtwo independent preys---existence and stability of equilibria, persistence conditions, etc. as well asuse numerical simulations in order to make comparison with the classical models, see e.g. [3]. Refernces: [1] A.J. Terry, A predator-prey model with generic birth and death rates forthe predator, Mathematical Biosciences 248 (2014) 57-66. [2] T. Ivanov, N. Dimitrova, A predator-prey model with generic birth and death rates for the predator and Beddington--DeAngelis functional response. Submitted. [3] R.K. Naji, A.T. Balasim, On the dynamical behavior of three species food web model,Chaos, Solitons and Fractals 34 (2007) 1636--1648.