HomCont

Description

HomCont, jointly developed with Alan Champneys (University of Bristol) and Yuri A Kuznetsov (Utrecht University), is a numerical toolbox for homoclinic bifurcation analysis. It is designed for use with AUTO written by Eusebius Doedel (Concordia University).

Specifically, HomCont deals with continuation of codimension-one heteroclinic and homoclinic orbits to hyperbolic and saddle-node equilibria, including the detection of many codimension-two singularities and the continuation of these singularities in three or more parameters.

Download

HomCont has been incorporated into the following AUTO and XPP versions:

Download AUTO97 [written in Fortran77]
Download AUTO2000 [written in C and Python]
Download AUTO-07p [written in Fortran95]
Download XPP [written by Bard Ermentrout (University of Pittsburgh)]

Instructions for the installation and usage can be found in the relevant AUTO manuals available for download below in the References section.You may also find the Online guide to AUTO constants [maintained by Sjors van der Stelt (CWI Amsterdam)] useful.

References

E Doedel, RC Paffenroth, AR Champneys, TF Fairgrieve, YA Kuznetsov, BE Oldeman, B Sandstede and X Wang.
AUTO2000: Continuation and bifurcation software for ordinary differential equations (with HOMCONT).
Technical report, Concordia University, 2002.
E Doedel, AR Champneys, TF Fairgrieve, YA Kuznetsov, B Sandstede and X Wang.
AUTO97: Continuation and bifurcation software for ordinary differential equations (with HOMCONT).
Technical report, Concordia University, 1997.
AR Champneys, YA Kuznetsov and B Sandstede.
A numerical toolbox for homoclinic bifurcation analysis.
International Journal of Bifurcation and Chaos 6 (1996) 867-887.
AR Champneys, YA Kutznetsov and B Sandstede.
HOMCONT: An AUTO86 driver for homoclinic bifurcation analysis (Version 2.0).
Technical Report AM-R9516, CWI Amsterdam, 1995.