The Numerical Detection of Hopf Bifurcation Points
During the computation of a one-parameter set of steady solutions to a time dependent problem, it is often of great interest to know when periodic behaviour can occur. This Hopf bifurcation is characterised by the linearisation about a steady state solution possessing a purely imaginary pair of eigenvalues. The cheap and reliable detection of such bifurcation is not however straightforward. The present paper examines the problem and suggests various strategies for solving it.
KeywordsHopf Bifurcation Invariant Subspace Krylov Subspace Negative Real Part Positive Real Part
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