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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 193143, 7 pages
http://dx.doi.org/10.1155/2014/193143
Research Article

Bifurcation in a Discrete Competition System

School of Science, Tianjin University of Commerce, Tianjin 300134, China

Received 9 February 2014; Accepted 9 April 2014; Published 28 April 2014

Academic Editor: Xiaochen Sun

Copyright © 2014 Li Xu et al. 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.

Abstract

A new difference system is induced from a differential competition system by different discrete methods. We give theoretical analysis for local bifurcation of the fixed points and derive the conditions under which the local bifurcations such as flip occur at the fixed points. Furthermore, one- and two-dimensional diffusion systems are given when diffusion terms are added. We provide the Turing instability conditions by linearization method and inner product technique for the diffusion system with periodic boundary conditions. A series of numerical simulations are performed that not only verify the theoretical analysis, but also display some interesting dynamics.