Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 432821, 17 pages
Research Article

Global Hopf Bifurcation Analysis for a Time-Delayed Model of Asset Prices

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 7 October 2009; Accepted 13 January 2010

Academic Editor: Xuezhong He

Copyright © 2010 Ying Qu and Junjie Wei. 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.


A time-delayed model of speculative asset markets is investigated to discuss the effect of time delay and market fraction of the fundamentalists on the dynamics of asset prices. It proves that a sequence of Hopf bifurcations occurs at the positive equilibrium v, the fundamental price of the asset, as the parameters vary. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined using normal form method and center manifold theory. Global existence of periodic solutions is established combining a global Hopf bifurcation theorem with a Bendixson's criterion for higher-dimensional ordinary differential equations.