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
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.