DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations

TL;DR

DDE-BIFTOOL is a MATLAB package designed for numerical bifurcation analysis of delay differential equations, supporting continuation, stability, and bifurcation detection of steady and periodic solutions.

Contribution

This paper introduces DDE-BIFTOOL, a comprehensive MATLAB toolkit for analyzing bifurcations in delay differential equations, including stability and bifurcation computations.

Findings

Supports continuation of steady and periodic solutions

Enables detection of various bifurcations including fold, Hopf, and torus bifurcations

Provides stability analysis through characteristic roots and Floquet multipliers

Abstract

DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with discrete constant and state-dependent delays. The package supports continuation and stability analysis of steady state solutions and periodic solutions. Further one can compute and continue several local and global bifurcations: fold and Hopf bifurcations of steady states; folds, period doublings and torus bifurcations of periodic orbits; and connecting orbits between equilibria. To analyse the stability of steady state solutions, approximations are computed to the rightmost, stability-determining roots of the characteristic equation which can subsequently be used as starting values in a Newton procedure. For periodic solutions, approximations to the Floquet multipliers are computed. The manual describes the structure of the package, its routines, and its data and method parameter structures.