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Continuation and Bifurcations: Numerical Techniques and Applications pp 227–246Cite as

The Numerical Detection of Hopf Bifurcation Points

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Part of the book series: NATO ASI Series ((ASIC,volume 313))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College, Queens’s Gate, London, SW7 2BZ, UK

    G. Moore

  2. School of Mathematical Sciences, University of Bath, Claverton Down, Bath, Avon. BA2, 7AY, UK

    T. J. Garratt & A. Spence

Authors
  1. G. Moore
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  2. T. J. Garratt
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  3. A. Spence
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium

    Dirk Roose

  2. Avery STDE, Turnhout, Belgium

    Bart De Dier

  3. School of Mathematical Sciences, University of Bath, Bath, UK

    Alastair Spence

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© 1990 Kluwer Academic Publishers

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Moore, G., Garratt, T.J., Spence, A. (1990). The Numerical Detection of Hopf Bifurcation Points. In: Roose, D., Dier, B.D., Spence, A. (eds) Continuation and Bifurcations: Numerical Techniques and Applications. NATO ASI Series, vol 313. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0659-4_15

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  • DOI: https://doi.org/10.1007/978-94-009-0659-4_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6781-2

  • Online ISBN: 978-94-009-0659-4

  • eBook Packages: Springer Book Archive

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