General functional response and recruitment in a predator–prey system with capture on both species

Abstract

This work provides a mathematical model for a predator‐prey system with general functional response and recruitment, which also includes capture on both species, and analyzes its qualitative dynamics. The model is formulated considering a population growth based on a general form of recruitment and predator functional response, as well as the capture on both prey and predators at a rate proportional to their populations. In this sense, it is proved that the dynamics and bifurcations are determined by a two‐dimensional threshold parameter. Finally, numerical simulations are performed using some ecological observations on two real species, which validate the theoretical results obtained. Copyright © 2014 John Wiley & Sons, Ltd.

Nonstandard finite difference schemes for a general predator–prey system

“…Let us consider the example of the predator-prey model presented in [21]. In this example Many numerical simulations, such as [2,3,8,10,11,12,13,31,32,35] .…”

“…We consider a mathematical model for a predator-prey system with general functional response and recruitment for both species [21]. The model is described by the system of nonlinear differential equations…”

“…Aiming at the conversion of continuous predator-prey models studied fully from the theoretical point of view to dynamically consistent discrete models, in the present paper we consider a mathematical model for a predator-prey system with general functional response and recruitment, which also includes capture on both species [21]. The results of qualitative aspects of the model are given in [21]. One important difference of this model in comparison with the above models is that the model [21] has one non-hyperbolic equilibrium point.…”

“…The results of qualitative aspects of the model are given in [21]. One important difference of this model in comparison with the above models is that the model [21] has one non-hyperbolic equilibrium point.…”

“…The paper is organized as follows. In Section 2 we recall from [21] the predator-prey system under consideration with the theoretical results of the existence of equilibrium points and their stability properties. In Section 3 we propose NSFD schemes and study their positivity and existence of equilibrium points.…”