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Journal of Applied Mathematics
Volume 2014, Article ID 852025, 10 pages
http://dx.doi.org/10.1155/2014/852025
Research Article

Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays

Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China

Received 9 November 2013; Accepted 4 April 2014; Published 4 May 2014

Academic Editor: Mehmet Sezer

Copyright © 2014 Xuhui Li. 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 competitive model of market structure with consumptive delays is considered. The local stability of the positive equilibrium and the existence of local Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equation. The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results.