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
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MARC

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100 1 |a Govaerts, Willy J. F. 
245 1 0 |a Numerical methods for bifurcations of dynamical equilibria /  |c Willy J.F. Govaerts. 
260 |a Philadelphia, Pa. :  |b Society for Industrial and Applied Mathematics,  |c c2000. 
300 |a xxii, 362 p. :  |b ill. ;  |c 26 cm. 
504 |a Includes bibliographical references and index. 
505 0 0 |t Nonlinear Equations and Dynamical Systems --  |t Examples from Population Dynamics --  |t Stable and Unstable Equilibria --  |t A Set of Bifurcation Points --  |t A Cusp Catastrophe --  |t A Hopf Bifurcation --  |t An Example from Combustion Theory --  |t Finite Element Discretization --  |t Finite Difference Discretization --  |t Numerical Continuation: Motivation by an Example --  |t An Example of Symmetry Breaking --  |t Linear and Nonlinear Stability --  |t Manifolds and Numerical Continuation --  |t Manifolds --  |t The Tangent Space --  |t Branches and Limit Points --  |t Numerical Continuation --  |t Natural Parameterization --  |t Pseudoarclength Continuation --  |t Steplength Control --  |t Convergence of Newton Iterates --  |t Some Practical Considerations --  |t Bordered Matrices --  |t Introduction: Motivation by Cramer's Rule --  |t The Construction of Nonsingular Bordered Matrices --  |t The Singular Value Inequality --  |t The Schur Inverse as Defining System for Rank Deficiency --  |t Invariant Subspaces of Parameter-Dependent Matrices --  |t Numerical Methods for Bordered Linear Systems --  |t Backward Stability --  |t Algorithm BEM for One-Bordered Systems --  |t Algorithm BEMW for Wider-Bordered Systems --  |t Generic Equilibrium Bifurcations in One-Parameter Problems --  |t Limit Points --  |t The Moore-Spence System for Quadratic Turning Points --  |t Quadratic Turning Points by Direct Bordering Methods --  |t Detection of Quadratic Turning Points --  |t Continuation of Limit Points --  |t Example: A One-Dimensional Continuous Brusselator --  |t The Model and Its Discretization --  |t Turning Points in the Brusselator Model. 
650 0 |a Differentiable dynamical systems. 
650 0 |a Differential equations  |x Numerical solutions. 
650 0 |a Bifurcation theory. 
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