HOMCONT, an AUTO86-based toolbox for homoclinic bifurcation analysis, is described in detail. The toolbox allows the continuation of codimension-one homoclinic orbits to hyperbolic and non-hyperbolic equilibria, as well as detection and continuation of higher-order homoclinic singularities in more parameters. All known codim 2 cases that involve a unique homoclinic orbit are supported, and certain heteroclinic computations are also possible. The document contains details on the various files supplied with HOMCONT and how to use them to analyse several tutorial examples.

Homoclinic and heteroclinic solutions (msc 34C37), General theory (msc 34Axx), Bifurcation (msc 34C23), Bifurcation theory (msc 34K18), Bifurcation (msc 35B32), Local and nonlocal bifurcation theory (msc 37Gxx), Bifurcation theory (msc 37H20), Bifurcation problems (msc 37J20), Bifurcation problems (msc 37K50), Normal forms, center manifold theory, bifurcation theory (msc 37L10), Computational methods for bifurcation problems (msc 37M20), Bifurcations and instability (msc 70K50)
Department of Analysis, Algebra and Geometry [AM]

Champneys, A.R, Kuznetsov, Y.A, & Sandstede, B. (1995). HomCont: An auto86 driver for homoclinic bifurcation analysis. Version 2.0. Department of Analysis, Algebra and Geometry [AM]. CWI.