Abstract and Applied Analysis

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

Xin-You Meng and Hai-Feng Huo

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 958140, 18 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048223

Digital Object Identifier
doi:10.1155/2014/958140

Mathematical Reviews number (MathSciNet)
MR3251546

Zentralblatt MATH identifier
07023398

Citation

Meng, Xin-You; Huo, Hai-Feng. Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 958140, 18 pages. doi:10.1155/2014/958140. https://projecteuclid.org/euclid.aaa/1425048223


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