Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 51406, 16 pages
doi:10.1155/2007/51406
Research Article
Dynamics of a Discretization Physiological Control System
Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
Received 31 May 2006; Revised 19 November 2006; Accepted 20 November 2006
Copyright © 2007 Xiaohua Ding and Huan Su. 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
We study the dynamics of solutions of discrete
physiological control system obtained by Midpoint rule. It is shown
that a sequence of Hopf bifurcations occurs at the positive
equilibrium as the delay increases and we analyze the stability of
the solution of the discrete system and calculate the direction of
the Hopf bifurcations. The numerical results are presented.