TW 330

K. Engelborghs, T. Luzyanina, G. Samaey
DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations

Abstract

DDE-BIFTOOL v. 2.00 is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with several constant and state-dependent delays. The package allows to compute, continue and analyse stability of steady state solutions and periodic solutions. It further allows to compute and continue steady state fold and Hopf bifurcations and to switch, from the latter, to an emanating branch of periodic solutions. Homoclinic and heteroclinic orbits can also be computed. To analyse the stability of steady state solutions, approximations are computed to the rightmost, stability-determining roots of the characteristic equation which can sub-sequently be used as starting values in a Newton procedure. For periodic solutions, approximations to the Floquet multipliers are computed. We describe the structure of the package, its routines, and its data and method parameter structures. We illustrate its use through a step-by-step analysis of several demo systems.