
Bifurcation Theory And Applications
World Scientific Publishing Co Pte Ltd
Published on 28. June 2005
Book
Paperback/Softback
392 pages
978-981-256-352-1 (ISBN)
Description
This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.
More details
Series
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 226 mm
Width: 155 mm
Thickness: 21 mm
Weight
562 gr
ISBN-13
978-981-256-352-1 (9789812563521)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Content
# Introduction to Steady State Bifurcation Theory # Introduction to Dynamic Bifurcation # Reduction Procedures and Stability # Steady State Bifurcation # Dynamic Bifurcation Theory: Finite Dimensional Case # Dynamic Bifurcation Theory: Infinite Dimensional Case # Bifurcations for Nonlinear Elliptic Equations # Reaction-Diffusion Equations # Pattern Formation and Wave Equations # Fluid Dynamics