A01=Shouhong Wang
A01=Tian Ma
Author_Shouhong Wang
Author_Tian Ma
Belousov-Zhabotinsky Reaction Equations
Cahn-Hillard Equation
Category=PBK
Dynamic Bifurcation
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Ginzburg Equation
Kuramoto-Sivashinsky Equation
Rayleigh-Benard Convection
Stability of Bifurcated Solutions
Stability of Invariant Compact Manifolds
Stability of Perturbed Systems
Steady State Bifurcation
Structure of Bifurcated Solutions
Taylor Problem
Product details
- ISBN 9789812562876
- Publication Date: 28 Jun 2005
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
