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Bifurcation: Analysis, Algorithms, Applications

Proceedings of the Conference at the University of Dortmund, August 18–22, 1986

  • Conference proceedings
  • © 1987

Overview

Editors:
  1. T. Küpper

    1. Institut für Angewandte Mathematik, Universität Hannover, Hannover 1, Germany

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  2. R. Seydel

    1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Germany

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  3. H. Troger

    1. Institut für Mechanik, Technische Universität Wien, Wien, Austria

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 79)

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Table of contents (36 papers)

  1. Front Matter

    Pages I-VIII
    Download chapter PDF

  2. The Effect of Discretization on Homoclinic Orbits

    • Wolf-Jürgen Beyn
    Pages 1-8

  3. Bifurcation in Elliptic Systems

    • Chris Budd
    Pages 9-17

  4. Transition to Asymmetric Convection Rolls

    • Friedrich H. Busse
    Pages 18-26

  5. Wave Patterns in Coupled Stationary Bifurcations with 0(2)-Symmetry

    • Gerhard Dangelmayr
    Pages 27-37

  6. Determination of Bifurcation Points and Catastrophes for the Brusselator Model with Two Parameters

    • Bart De Dier, Dirk Roose
    Pages 38-46

  7. Numerical Studies of Bifurcation in Reaction-Diffusion Models Using Pseudo-Spectral and Path-Following Methods

    • J. C. Eilbeck
    Pages 47-60

  8. A quick multiparameter test for periodic solutions

    • Bernold Fiedler, Peter Kunkel
    Pages 61-70

  9. Codimension Two Bifurcations Near an Invariant n-Torus

    • Dietrich Flockerzi
    Pages 71-82

  10. Hopf Bifurcation in the Drilling Process under Regenerative Cutting Conditions

    • Mustapha S. Fofana
    Pages 83-89

  11. Critical Points of Mixed Fluids and their Numerical Treatment

    • A. Griewank, P. Rabier
    Pages 90-97

  12. Bifurcation Theory in Physics: Recent Trends and Problems

    • Werner Güttinger
    Pages 98-113

  13. An Application of Complex Bifurcation to a Problem in Computer Graphics

    • Michael E. Henderson
    Pages 114-121

  14. Continuation of Periodic Solutions in Parabolic Partial Differential Equations

    • Martin Holodniok, P. Knedlík, M. Kubíček
    Pages 122-130

  15. Bifurcation in Degenerate Directions

    • Edgar Jäger
    Pages 131-138

  16. On Cornu Spirals. Disorder, Selfsimilarity, and Jacobi’s θ3(ν,τ)

    • Nicholas D. Kazarinoff, Evangelos A. Coutsias
    Pages 139-152

  17. Optimization in Bifurcation Problems using a Continuation Method

    • J. P. Kernévez, E. J. Doedel
    Pages 153-160

  18. On the Numerical Study of Bifurcation Problems

    • Edwin J. Kreuzer
    Pages 161-171

  19. External Forcing in a Glycolytic Model

    • Magnus Küper
    Pages 172-176

  20. Some Remarks on the Morphology of Non-Unique Solutions in Nonlinear Elastostatics

    • Franz Karl Labisch
    Pages 177-184
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Keywords

About this book

The conference on BIFURCATIONS: ANALYSIS, ALGORITHMS, APPLICATIONS took place in Dortmund in August 18 - 22, 1986. More then 150 Scientists from 16 countries participated in the meeting, among them mathematicians, engi­ neers, and physicists. A broad spectrum of new results on bifurcation was covered by 49 talks. The diversity of the range of treated topics and of involved fields inspired fruitful discussions. 36 refereed papers are contained in these proceedings. The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. The more theoreti­ cal papers include the topics symmetry breaking, delay differential equations, Cornu spirals, homoclinic orbits, and selfsimilarity. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec­ trum, complex bifurcation, and bifurcation near tori. Several numerical as­ pects are discussed, among them continuation, block elimination, and spectral methods. Algorithms are proposed for approximating manifolds, calculating pe­ riodic solutions and handling multi-parameter problems. Ample space is devoted to· applications. Classical phenomena from fluid mechanics (such as convection rolls and th~ Taylor vortex problem), buckling, and reaction-diffusion pro­ blems are considered. Other applications of bifurcations include railway vehicle dynamics, computer graphics, semiconductors, drilling processes, simu­ lation of oil reservoirs, and rotor dynamics. The proceedings reflect current research in bifurcation. They are an attempt to bring together researchers from differ~nt disciplines to stimulate common effort towards a better understanding and handling of bifurcation pro­ blems.

Editors and Affiliations

  • Institut für Angewandte Mathematik, Universität Hannover, Hannover 1, Germany

    T. Küpper

  • Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Germany

    R. Seydel

  • Institut für Mechanik, Technische Universität Wien, Wien, Austria

    H. Troger

Bibliographic Information

  • Book Title: Bifurcation: Analysis, Algorithms, Applications

  • Book Subtitle: Proceedings of the Conference at the University of Dortmund, August 18–22, 1986

  • Editors: T. Küpper, R. Seydel, H. Troger

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7241-6

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1987

  • Hardcover ISBN: 978-3-7643-1798-0Due: 01 January 1987

  • Softcover ISBN: 978-3-0348-7243-0Published: 12 February 2012

  • eBook ISBN: 978-3-0348-7241-6Published: 08 March 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: VIII, 360

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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