Allee effect in a discrete-time predator-prey system


Celik C. , Duman O.

CHAOS SOLITONS & FRACTALS, vol.40, no.4, pp.1956-1962, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 4
  • Publication Date: 2009
  • Doi Number: 10.1016/j.chaos.2007.09.077
  • Title of Journal : CHAOS SOLITONS & FRACTALS
  • Page Numbers: pp.1956-1962

Abstract

In this paper, we study the stability of a discrete-time predator-prey system with and without Allee effect. By analyzing both systems, we first obtain local stability conditions of the equilibrium points without the Allee effect and then exhibit the impact of the Allee effect on stability when it is imposed on prey population. We also show the stabilizing effect of Allee effect by numerical simulations and verify that when the prey population is subject to an Allee effect, the trajectory of the solutions approximates to the corresponding equilibrium point much faster. Furthermore, for some fixed parameter values satisfying necessary conditions, we show that the corresponding equilibrium point moves from instability to stability under the Allee effect on prey population. (C) 2007 Elsevier Ltd. All rights reserved.