IMPROVED DETECTION OF BIFURCATIONS IN LARGE NONLINEAR SYSTEMS VIA THE CONTINUATION OF INVARIANT SUBSPACES ALGORITHM

Abstract

The Continuation of Invariant Subspaces (CIS) algorithm [Demmel et al., 2001; Dieci & Friedman, 2001] produces a smooth orthogonal similarity transformation to block triangular form of a parameter dependent matrix A(s). The CIS algorithm is an adaptation of an iterative refinement technique for improving the accuracy of computed invariant subspaces. On the basis of the CIS algorithm, new test functions are defined for an improved, more reliable detection of bifurcations in problems with simple bifurcations near multiple bifurcations, problems with multiple bifurcations, and problems with symmetries. Illustrative examples are given.