Numerical computation of bifurcations in large equilibrium systems in matlab

• Autores: D. Bindel, M. Friedman, Willy Joseph Florent Govaerts, J. Hughes, Yu. A. Kuznetsov
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 261, Nº 1, 2014, págs. 232-248
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.10.034
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• Resumen

  • The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly-varying basis for an invariant subspace R(s) of a parameter-dependent matrix A(s). We have incorporated the CIS algorithm into Cl_matcont, a Matlab package for the study of dynamical systems and their bifurcations. Using subspace reduction, we extend the functionality of Cl_matcont to large-scale computations of bifurcations of equilibria. In this paper, we describe the algorithms and functionality of the resulting Matlab bifurcation package Cl_matcontL. The novel features include: new CIS-based, continuous, well-scaled test functions for codimension 1 and 2 bifurcations; detailed description of locators for large problems; and examples of bifurcation analysis in large sparse problems.