Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations

We present a numerical technique for the stability analysis and the computation of branches of Hopf bifurcation points in nonlinear systems of delay differential equations with several constant delays. The stability analysis of a steady-state solution is done by a numerical implementation of the argument principle, which allows to compute the number of eigenvalues with positive real part of the characteristic matrix. The technique is also used to detect bifurcations of higher singularity (Hopf and fold bifurcations) during the continuation of a branch of Hopf points. This allows to trace new branches of Hopf points and fold points.