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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 290497, 6 pages
http://dx.doi.org/10.1155/2013/290497
Research Article

Hopf Bifurcation Analysis for the Modified Rayleigh Price Model with Time Delay

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Received 9 May 2013; Accepted 28 June 2013

Academic Editor: Sakthivel Rathinasamy

Copyright © 2013 Yanhui Zhai 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

This paper mainly modifies and further develops the Reyleigh price model. By modifying the basic Reyleigh model, we can more accurately illustrate the economic phenomena with price varying. First, we research the dynamics of the modified Reyleigh model with time delay. By employing the normal form theory and center manifold theory, we obtain some testable results on these issues. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. Finally, some numerical simulations are given to illustrate the effectiveness of our results.