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:
Online Access:Table of contents
Publisher description
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.