Normal Forms And Bifurcation Of Planar Vector Fields
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Normal Forms And Bifurcation Of Planar Vector Fields
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Author : Shui-Nee Chow
language : en
Publisher: Cambridge University Press
Release Date : 1994-07-29
Normal Forms And Bifurcation Of Planar Vector Fields written by Shui-Nee Chow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-29 with Mathematics categories.
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.
Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem
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Author : Robert Roussarie
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-26
Bifurcations Of Planar Vector Fields And Hilbert S Sixteenth Problem written by Robert Roussarie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)
Bifurcations Of Planar Vector Fields
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Author : Jean-Pierre Francoise
language : en
Publisher: Springer
Release Date : 2006-11-14
Bifurcations Of Planar Vector Fields written by Jean-Pierre Francoise and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Bifurcations Of Planar Vector Fields
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Author : Freddy Dumortier
language : en
Publisher: Springer
Release Date : 2006-12-08
Bifurcations Of Planar Vector Fields written by Freddy Dumortier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena.
Bifurcation Of Planar Vector Fields And Hilbert S Sixteenth Problem
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Author : Robert H. Roussarie
language : en
Publisher: Birkhauser
Release Date : 1998
Bifurcation Of Planar Vector Fields And Hilbert S Sixteenth Problem written by Robert H. Roussarie and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.
Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles
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Author : Maoan Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Normal Forms Melnikov Functions And Bifurcations Of Limit Cycles written by Maoan Han and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
Bifurcations Of Planar Vector Fields
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Author : Freddy Dumortier
language : en
Publisher: Springer
Release Date : 1991
Bifurcations Of Planar Vector Fields written by Freddy Dumortier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena.
Normal Forms Bifurcations And Finiteness Problems In Differential Equations
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Author : Christiane Rousseau
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29
Normal Forms Bifurcations And Finiteness Problems In Differential Equations written by Christiane Rousseau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-29 with Mathematics categories.
Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
Bifurcations And Periodic Orbits Of Vector Fields
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Author : Dana Schlomiuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Bifurcations And Periodic Orbits Of Vector Fields written by Dana Schlomiuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Nonlinear Systems Vol 1
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Author : Victoriano Carmona
language : en
Publisher: Springer
Release Date : 2018-09-15
Nonlinear Systems Vol 1 written by Victoriano Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-15 with Science categories.
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.