Bifurcation Theory and Applications PDF Download. Download free ebook of Bifurcation Theory and Applications in PDF format or read online by Tian Ma,Shouhong Wang 9789814480598 Published on 2005-06-27 by World Scientific
' 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. Contents:Introduction to Steady State Bifurcation TheoryIntroduction to Dynamic BifurcationReduction Procedures and StabilitySteady State BifurcationDynamic Bifurcation Theory: Finite Dimensional CaseDynamic Bifurcation Theory: Infinite Dimensional CaseBifurcations for Nonlinear Elliptic EquationsReaction-Diffusion EquationsPattern Formation and Wave EquationsFluid Dynamics Readership: Graduate students and researchers in mathematics, physics, chemistry, biology and engineering. Keywords:Dynamic Bifurcation;Steady State Bifurcation;Stability of Bifurcated Solutions;Structure of Bifurcated Solutions;Stability of Invariant Compact Manifolds;Stability of Perturbed Systems;Belousov-Zhabotinsky Reaction Equations, Kuramoto-Sivashinsky Equation;Cahn-Hillard Equation;Ginzburg Equation;Rayleigh-Benard Convection;Taylor ProblemKey Features:Provides a comprehensive and intuitive review of existing bifurcation theoriesNew theories for bifurcations from eigenvalues with even multiplicityGeneral recipes for applicationsReviews:“The book provides a nice introduction to a variety of bifurcation problems …”Mathematical Reviews '
This Book was ranked at 38 by Google Books for keyword Chaos Theory.
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Book which was published by World Scientific since 2005-06-27 have ISBNs, ISBN 13 Code is 9789814480598 and ISBN 10 Code is 9814480592
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