This book is mainly concerned with the bifurcation theory of ODEs. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: center manifold theory and normal form theory, by which one may reduce the dimension of equations and change forms of equations to be as simple as possible. Chapters 3-5 of the book study in considerable detail the bifurcation of those one or two dimensional equations with one, two or several parameters.
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Book Description
Editorial Reviews
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"I cordially recommend the book to researchers new to this field." Henk Broer, Bulletin of the American Mathematical Society
"This book is clearly written, replete with biographical notes, and careful in its rigor. It is a must for anyone interested in ordinary differential equations of bifurcation theory." Kennneth R. Meyer, SIAM Review
"...The presentation in the book enters into fine detail and is rather complete..." Mathematical Reviews
"This book is clearly written, replete with biographical notes, and careful in its rigor. It is a must for anyone interested in ordinary differential equations of bifurcation theory." Kennneth R. Meyer, SIAM Review
"...The presentation in the book enters into fine detail and is rather complete..." Mathematical Reviews
Book Description
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.
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Inside This Book
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First Sentence:
The main goal of this book is to study some bifurcation phenomena of vector fields. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
homoclinic loop bifurcation, miniversal deformation, global center manifold, double limit cycle bifurcation, resonant monomials, matrix representation method, nonzero equilibria, local center manifold, symplectic operator, three limit cycles, orthogonal complementary subspace, normal form equation, versal deformations, double zero eigenvalue, normal form theory, planar vector fields, unique limit cycle, homoclinic bifurcation, symplectic vector space, reverse lexicographic, center manifolds, weak focus, bifurcation surface, center manifold theory, semisimple part Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Bibliographical Notes, Proof Let, Takens's Theorem, Double Zero Eigenvalue, Malgrange Preparation Theorem, Hence Ker New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The main goal of this book is to study some bifurcation phenomena of vector fields. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
homoclinic loop bifurcation, miniversal deformation, global center manifold, double limit cycle bifurcation, resonant monomials, matrix representation method, nonzero equilibria, local center manifold, symplectic operator, three limit cycles, orthogonal complementary subspace, normal form equation, versal deformations, double zero eigenvalue, normal form theory, planar vector fields, unique limit cycle, homoclinic bifurcation, symplectic vector space, reverse lexicographic, center manifolds, weak focus, bifurcation surface, center manifold theory, semisimple part Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Bibliographical Notes, Proof Let, Takens's Theorem, Double Zero Eigenvalue, Malgrange Preparation Theorem, Hence Ker New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 24
books:
See all 24 books this book cites
5
books
cite this book:
- Nonlinear Dynamics by Helleman in Back Matter (1), and Back Matter (2)
- Differential Equations (2nd Edition) by John Polking in Back Matter
- Lie Algebras (Pure & Applied Mathematics Monograph) by Zhexian Wan in Back Matter
- Nonlinear Differential Equations by Jack K. Hale in Back Matter
- Dynamics of Feedback Systems by Alistair I. Mees in Back Matter
See all 24 books this book cites
- Ordinary Differential Equations with Applications by Carmen Chicone in Back Matter
- Controlling Chaos and Bifurcations in Engineering Systems by Guanrong Chen on page 231
- Global Bifurcation Theory and Hilbert's Sixteenth Problem (Mathematics and Its Applications) by V. Gaiko in Back Matter
- Advances in Computational Mathematics (Lecture Notes in Pure and Applied Mathematics) by Zhongying Chen on page 392
- Ordinary Differential Equations with Applications (Texts in Applied Mathematics) by Carmen Chicone on page 607
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