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Numerical methods for bifurcat...
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Numerical methods for bifurcations of dynamical equilibria / Willy J.F. Govaerts.
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Bibliographic Details
Main Author:
Govaerts, Willy J. F.
Format:
Book
Language:
English
Published:
Philadelphia, Pa. :
Society for Industrial and Applied Mathematics,
c2000.
Subjects:
Differentiable dynamical systems.
Differential equations
>
Numerical solutions.
Bifurcation theory.
Online Access:
Table of contents
Publisher description
Holdings
Description
Table of Contents
Staff View
Table of 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.
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