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Abstract and Applied Analysis
Volume 2014, Article ID 958140, 18 pages
http://dx.doi.org/10.1155/2014/958140
Research Article

Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays

School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 18 April 2014; Revised 15 June 2014; Accepted 16 June 2014; Published 14 August 2014

Academic Editor: Yongli Song

Copyright © 2014 Xin-You Meng and Hai-Feng Huo. 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 class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998). Numerical simulations are given to support the theoretical results.