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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 847360, 16 pages
Research Article

Basins of Attraction for Two-Species Competitive Model with Quadratic Terms and the Singular Allee Effect

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Received 26 August 2014; Accepted 29 October 2014

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 A. Brett and M. R. S. Kulenović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the following system of difference equations: where , , , , are positive constants and are initial conditions. This system has interesting dynamics and it can have up to seven equilibrium points as well as a singular point at , which always possesses a basin of attraction. We characterize the basins of attractions of all equilibrium points as well as the singular point at and thus describe the global dynamics of this system. Since the singular point at always possesses a basin of attraction this system exhibits Allee’s effect.