Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay

Abstract

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.