Abstract and Applied Analysis
Volume 2011 (2011), Article ID 980686, 10 pages
http://dx.doi.org/10.1155/2011/980686
Research Article

Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays

Bao Shi,1 Fangwei Zhang,1 and Shihe Xu2

1Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, China
2Department of Mathematics, Zhaoqing University, Zhaoqing, Guangdong 526061, China

Received 3 November 2010; Accepted 25 January 2011

Academic Editor: Allan C. Peterson

Copyright © 2011 Bao Shi 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

A mathematical model for growth of tumors with two discrete delays is studied. The delays, respectively, represent the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis and kill of cells by the inhibitor. We show the influence of time delays on the Hopf bifurcation when one of delays is used as a bifurcation parameter.