Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation

Abstract

For the Dirichlet boundary value problem of the diffusive Nicholson's blowflies equation, it was shown in Ref. [17] that in a certain range of the parameter space, there is a unique positive steady state solution. In this paper, we propose a scheme to compute this steady state numerically. In addition, we describe an iterative procedure to locate the critical values of the delay where a Hopf bifurcation of time periodic solutions takes place near the steady state. Some numerical simulations of both schemes are given.