Numerical computation of bifurcations in large equilibrium systems in MATLAB

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. (C) 2013 Elsevier B.V. All rights reserved.