UK Nonlinear News , May 1997.

AUTO97 and the Homoclinic Orbit Software HomCont

By Alan Champneys

The latest version of Sebius Doedel's AUTO software package for numerical continuation and bifurcation analysis of ordinary differential equations is now available (via ftp from ftp://ftp.cs.concordia.ca/pub/doedel/auto). Compared to the previous release (AUTO94) there have been only minor functional changes, but the manual has been significantly updated and integrated for the first time is HomCont.

HomCont is a collection of subroutines for the continuation in two or more parameters of homoclinic solutions to equilibria in ODEs. The accurate detection and multi-parameter continuation of certain codimension-two singularities is allowed for, including all known cases that involve a unique homoclinic orbit at the singular point. Homoclinic connections to hyperbolic and non-hyperbolic equilibria are allowed as are certain heteroclinic orbits, and homoclinic orbits in Hamiltonian and reversible systems. The current implementation of HomCont must be considered as experimental, and updates are anticipated.

For a description of the capabilities of and methods behind HomCont see Chapter 16 of the AUTO97 manual or the papers:

  1. Champneys, A.R. & Kuznetsov, Yu.A. 1994 International Journal of Bifurcation & Chaos, 4:785-822.
  2. Champneys, A.R., Kuznetsov, Yu.A. & Sandstede, B. 1996 International Journal of Bifurcation & Chaos, 6:867-887.

For further information concerning HomCont, especially practical questions arising in trying to use it contact Alan Champneys ( a.r.champneys@bristol.ac.uk).



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