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 AUTO-07p [written in Fortran95]
Download AUTO2000 [written in C and Python]
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; the manual for AUTO-07P can be found as auto/07p/doc/auto.pdf in the downloaded AUTO-07p source code. 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.