Numerical Computation of Stability and Detection of Hopf Bifurcations of Steady State Solutions of Delay Diierential Equations Koen Engelborghs Numerical Computation of Stability and Detection of Hopf Bifurcations of Steady State Solutions of Delay Diierential Equations Koen Engelborghs

The characteristic equation of a system of delay diierential equations (DDEs) is a nonlinear equation with innnitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e. stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight in the systems behaviour, can be used for robust bifurca-tion detection and for eecient indirect calculation of bifurcations points.