The Numerical Detection of Hopf Bifurcation Points

  • G. Moore
  • T. J. Garratt
  • A. Spence
Part of the NATO ASI Series book series (ASIC, volume 313)


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.


Hopf Bifurcation Invariant Subspace Krylov Subspace Negative Real Part Positive Real Part 
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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • G. Moore
    • 1
  • T. J. Garratt
    • 2
  • A. Spence
    • 2
  1. 1.Department of MathematicsImperial CollegeLondonUK
  2. 2.School of Mathematical SciencesUniversity of BathBathUK

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