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Numerical methods for bifurcations of dynamical equilibria

Author: Willy J F Govaerts
Publisher: Philadelphia, Pa. : Society for Industrial and Applied Mathematics, ©2000.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Willy J F Govaerts
ISBN: 0898714427 9780898714425
OCLC Number: 42290210
Description: xxii, 362 pages : illustrations ; 26 cm
Contents: Nonlinear Equations and Dynamical Systems --
Examples from Population Dynamics --
Stable and Unstable Equilibria --
A Set of Bifurcation Points --
A Cusp Catastrophe --
A Hopf Bifurcation --
An Example from Combustion Theory --
Finite Element Discretization --
Finite Difference Discretization --
Numerical Continuation: Motivation by an Example --
An Example of Symmetry Breaking --
Linear and Nonlinear Stability --
Manifolds and Numerical Continuation --
Manifolds --
The Tangent Space --
Branches and Limit Points --
Numerical Continuation --
Natural Parameterization --
Pseudoarclength Continuation --
Steplength Control --
Convergence of Newton Iterates --
Some Practical Considerations --
Bordered Matrices --
Introduction: Motivation by Cramer's Rule --
The Construction of Nonsingular Bordered Matrices --
The Singular Value Inequality --
The Schur Inverse as Defining System for Rank Deficiency --
Invariant Subspaces of Parameter-Dependent Matrices --
Numerical Methods for Bordered Linear Systems --
Backward Stability --
Algorithm BEM for One-Bordered Systems --
Algorithm BEMW for Wider-Bordered Systems --
Generic Equilibrium Bifurcations in One-Parameter Problems --
Limit Points --
The Moore-Spence System for Quadratic Turning Points --
Quadratic Turning Points by Direct Bordering Methods --
Detection of Quadratic Turning Points --
Continuation of Limit Points --
Example: A One-Dimensional Continuous Brusselator --
The Model and Its Discretization --
Turning Points in the Brusselator Model.
Responsibility: Willy J.F. Govaerts.
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