Continuation of homoclinic orbits in MATLAB

Authors:
M. Friedman;W. Govaerts;Yu. A. Kuznetsov;B. Sautois
Affiliations:
Mathematical Sciences Department, University of Alabama, Huntsville, AL;Department of Applied Mathematics and Computer Science, Ghent University, Ghent, Belgium;Mathematisch Instituut, Utrecht, The Netherlands;Department of Applied Mathematics and Computer Science, Ghent University, Ghent, Belgium
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

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Abstract

We have added the functionality for continuing homoclinic orbits to cl_matcont, a user-friendly matlab package for the study of dynamical systems and their bifurcations. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits. The implementation is done using the continuation of invariant subspaces, with the Ricatti equations included in the defining system. The continuation can be initiated from a limit cycle with large period or from a Bogdanov-Takens point. All known codimension-two bifurcations are tested for, during continuation. The test functions for inclination-flip bifurcations are implemented in a new and more efficient way.