Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems

Tuckerman Laurette S. Doedel Eusebius

ISBN 10: 0387989706 / ISBN 13: 9780387989709

Verlag: Springer, 2000

Beschreibung

pp. x + 471.

Bestandsnummer des Verkäufers 183875945

Bibliografische Details

• Titel: Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems
• Verlag: Springer
• Veröffentlichungsdatum: 2000
• Sprache: Englisch
• ISBN-10: 0387989706
• ISBN-13: 9780387989709
• Bindung: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

Numerical bifurcation techniques for chemical reactor problems.- Path-following of large bifurcation problems with iterative methods.- On the bifurcation from continuous to segmented chip formation in metal cutting.- Using dynamical system tools in Matlab.- Formation and instabilities of coherent structures in channel flows.- Applications of smooth orthogonal factorizations of matrices.- Continuation of codimension-2 equilibrium bifurcations in Content.- Inclination-flips in the unfolding of a singular heteroclinic cycle.- Investigating torus bifurcations in the forced Van der Pol oscillator.- Quasiperiodic response to parametric excitations.- Self-organized criticality: analysis and simulation of a ID sandpile.- Computation and bifurcation analysis of periodic solutions of large-scale systems.- Multiple equilibria and stability of the north-atlantic wind-driven ocean circulation.- Numerical exploration of bifurcation phenomena associated with complex instability.- Chaos in traveling waves of lattice systems of unbounded media.- Pattern formation in a cellular slime mold.- Global parametrization and computation of resonance surfaces for periodically forced oscillators.- Computing invariant tori and circles in dynamical systems.- A Design problem for image processing.- Bifurcation analysis for timesteppers.- List of participants.

Reseña del editor

The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.