Structurally Unstable Quadratic Vector Fields Of Codimension One
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Structurally Unstable Quadratic Vector Fields Of Codimension One
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Author : Joan C. Artés
language : en
Publisher: Springer
Release Date : 2018-06-28
Structurally Unstable Quadratic Vector Fields Of Codimension One written by Joan C. Artés and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Mathematics categories.
Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors’ work on structurally stable planar quadratic polynomial differential systems. In the present work the authors aim at finding all possible phase portraits in the Poincaré disc, modulo limit cycles, of planar quadratic polynomial differential systems manifesting the simplest level of structural instability. They prove that there are at most 211 and at least 204 of them.
Structurally Stable Quadratic Vector Fields
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Author : Joan C. Artés
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Structurally Stable Quadratic Vector Fields written by Joan C. Artés and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book solves a problem that has been open for over 20 years--the complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the more than 800 papers that have been published on the subject. One of the problems in the qualitative theory of quadratic vector fields is the classification of all structurally stable ones: In this work the authors solve this problem completely modulo limit cycles and give all possible phase portraits for such structurally stable quadratic vector fields.
Structurally Stable Quadratic Vector Fields
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Author : Joan C. Arts
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-06-29
Structurally Stable Quadratic Vector Fields written by Joan C. Arts and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-29 with Mathematics categories.
This book solves a problem that has been open for over 20 years--the complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the more than 800 papers that have been published on the subject. One of the problems in the qualitative theory of quadratic vector fields is the classification of all structurally stable ones: In this work the authors solve this problem completely modulo limit cycles and give all possible phase portraits for such structurally stable quadratic vector fields.
Geometric Configurations Of Singularities Of Planar Polynomial Differential Systems
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Author : Joan C. Artés
language : en
Publisher: Springer Nature
Release Date : 2021-07-19
Geometric Configurations Of Singularities Of Planar Polynomial Differential Systems written by Joan C. Artés and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-19 with Mathematics categories.
This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.
Dynamics And Bifurcations
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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamics And Bifurcations written by Jack K. Hale 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 2012-12-06 with Mathematics categories.
In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
Modeling In Fluid Mechanics
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Author : Igor Gaissinski
language : en
Publisher: CRC Press
Release Date : 2018-06-13
Modeling In Fluid Mechanics written by Igor Gaissinski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-13 with Mathematics categories.
This volume is dedicated to modeling in fluid mechanics and is divided into four chapters, which contain a significant number of useful exercises with solutions. The authors provide relatively complete references on relevant topics in the bibliography at the end of each chapter.
Computational Differentiation
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Author : M. Berz
language : en
Publisher: Soc for Industrial & Applied Math
Release Date : 1996
Computational Differentiation written by M. Berz and has been published by Soc for Industrial & Applied Math this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computers categories.
This volume encompasses both the automatic transformation of computer programs as well as the methodologies for the efficient exploitation of mathematical underpinnings or program structure.
Bifurcations
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Author : Takashi Matsumoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Bifurcations written by Takashi Matsumoto 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 2012-12-06 with Mathematics categories.
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Computational Methods For The Atmosphere And The Oceans
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Author : Roger Temam
language : en
Publisher: Elsevier
Release Date : 2009-06-16
Computational Methods For The Atmosphere And The Oceans written by Roger Temam and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-16 with Computers categories.
This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered. • Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics • Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences• Contributions uniquely address central problems and provide a survey of the frontier of research