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Continuation of homoclinic orbits in MATLAB. (English) Zbl 1129.65324
Sunderam, Vaidy S. (ed.) et al., Computational science – ICCS 2005. 5th international conference, Atlanta, GA, USA, May 22–25, 2005. Proceedings, Part I. Berlin: Springer (ISBN 3-540-26032-3/pbk). Lecture Notes in Computer Science 3514, 263-270 (2005).
Summary: 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 Riccati 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.
For the entire collection see [Zbl 1073.68012].

MSC:
65P30 Numerical bifurcation problems
65Y15 Packaged methods for numerical algorithms
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