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Numerical Methods for Bifurcations of Dynamical Equilibria

Numerical Methods for Bifurcations of Dynamical Equilibria

  • Date Published: January 1987
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898714425

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About the Authors
  • Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra. Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to fundamental cases covered by the equivariant branching lemma.

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    Product details

    • Date Published: January 1987
    • format: Paperback
    • isbn: 9780898714425
    • length: 384 pages
    • dimensions: 252 x 176 x 18 mm
    • weight: 0.672kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    Notation
    Introduction
    1. Examples and Motivation
    2. Manifolds and Numerical Continuation
    3. Bordered Matrices
    4. Generic Equilibrium Bifurcations in One-Parameter Problems
    5. Bifurcations Determined by the Jordan Form of the Jacobian
    6. Singularity Theory
    7. Singularity Theory with a Distinguished Bifurcation Parameter
    8. Symmetry-Breaking Bifurcations
    9. Bifurcations with Degeneracies in the Nonlinear Terms
    10. An Introduction to Large Dynamical Systems
    Bibliography
    Index.

  • Author

    Willy J. F. Govaerts, Universiteit Gent, Belgium

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