A nonstandard numerical scheme for a predator-prey model with Allee effect

Ongun M., Ozdogan N.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, vol.10, no.2, pp.713-723, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.22436/jnsa.010.02.32
  • Journal Name: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), zbMATH
  • Page Numbers: pp.713-723
  • Keywords: Allee effect, stability analysis, nonstandard finite difference scheme, predator-prey model, STABILITY, DYNAMICS, SYSTEMS
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this paper, we present a Lotka-Volterra predator-prey model with Allee effect. This system with general functional response has an Allee effect on prey population. A nonstandard finite difference scheme is constructed to transform the continuous time predator-prey model with Allee effect into the discrete time model. We use the Schur-Cohn criteria which deal with coefficients of the characteristic polynomial for determining the stability of discrete time system. The proposed numerical schemes preserve the positivity of the solutions with positive initial conditions. The new discrete-time model shows dynamic consistency with continuous-time model. (C) 2017 All rights reserved.