Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 19413, 12 pages

Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay

Xiaohua Ding and Wenxue Li

Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Received 31 December 2005; Accepted 13 March 2006

Copyright © 2006 Xiaohua Ding and Wenxue 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.


A kind of discrete system according to Nicholson's blowflies equation with a finite delay is obtained by the Euler forward method, and the dynamics of this discrete system are investigated. Applying the theory of normal form and center manifold, we not only discuss the linear stability of the equilibrium and the existence of the local Hopf bifurcations, but also give the explicit algorithm for determining the direction of bifurcation and stability of the periodic solution of bifurcation.