Friedman, M.; Govaerts, W.; Kuznetsov, Yu. A.; Sautois, B. 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]. Cited in 4 Documents MSC: 65P30 Numerical bifurcation problems 65Y15 Packaged methods for numerical algorithms Software:CL_MATCONT; AUTO2000; AUTO; Matlab; MATCONT; HomCont PDFBibTeX XMLCite \textit{M. Friedman} et al., Lect. Notes Comput. Sci. 3514, 263--270 (2005; Zbl 1129.65324) Full Text: DOI