STABILITY ANALYSIS OF THE GURTIN—MACCAMY MODEL

摘要

In this paper we propose a numerical scheme to investigate the stability of steadystates of the nonlinear Gurtin–MacCamy system, which is a basic model in population dynamics.In fact the analysis of stability is usually performed by the study of transcendental characteristicequations that are too difficult to approach by analytical methods. The method is based on thediscretization of the infinitesimal generator associated to the semigroup of the solution operator byusing pseudospectral differencing techniques. The method computes the rightmost characteristicroots, and it is shown to converge with spectral accuracy behavior.