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9780898714425 Academic Inspection Copy

Numerical Methods for Bifurcations of Dynamical Equilibria

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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 bifurations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical method 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 the fundamental cases covered by the equivariant branching lemma.
Preface Notation Introduction Chapter 1: Examples and Motivation Chapter 2: Manifolds and Numerical Continuation Chapter 3: Bordered Matrices Chapter 4: Generic Equilibrium Bifurcations in One-Parameter Problems Chapter 5: Bifurcations Determined by the Jordan Form of the Jacobian Chapter 6: Singularity Theory Chapter 7: Singularity Theory with a Distinguished Bifurcation Parameter Chapter 8: Symmetry-Breaking Bifurcations Chapter 9: Bifurcations with Degeneracies in the Nonlinear Terms Chapter 10: An Introduction to Large Dynamical Systems Bibliography Index.
Numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems.
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