On the Location and Continuation of Hopf bifurcations in Large-Scale Problems

CL_MATCONT is a MATLAB package for the study of dynamical systems and their bifurcations. It uses a minimally augmented system for continuation of the Hopf curve. The Continuation of Invariant Subspaces (CIS) algorithm produces a smooth orthonormal basis for an invariant subspace R(s) of a parameter-dependent matrix A(s). We extend a minimally augmented system technique for location and continuation of Hopf bifurcations to large-scale problems using the CIS algorithm, which has been incorporated into CL_MATCONT. We compare this approach with using a standard augmented system and show that a minimally augmented system technique is more suitable for large-scale problems. We also suggest an improvement of a minimally augmented system technique for the case of the torus continuation.

• Type: Journal
• Year: 2008
• Where: IJBC
• Authors: M. Friedman, W. Qiu
• Keywords: IJBC 2008, Invariant Subspace, Large-scale Problems, Smooth Orthonormal Basis