Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations (Q1923470)

A numerical technique for the stability analysis and the computation of branches of Hopf bifurcation points in systems of nonlinear delay differential equations (DDE) with several constant delays is presented. This technique is implemented within the LOCBIF software package. The stability analysis of a steady-state solution of the system of DDEs is done by the eigenvalues with positive real part of the characteristic matrix. The application of this method to the stability analysis of Hopf bifurcation points is quite efficient. The use of a determining system for Hopf bifurcation points allows to trace branches of Hopf points via continuation.