Structurally Unstable Quadratic Vector Fields Of Codimension One

Author : Joan C. Artés
Publisher : Springer
ISBN 13 : 3319921177
Total Pages : 267 pages
Book Rating : 4.74/5 ( download)

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Download or read book Structurally Unstable Quadratic Vector Fields of Codimension One written by Joan C. Artés and published by Springer. This book was released on 2018-06-28 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joan C. Artés
Publisher : American Mathematical Soc.
ISBN 13 : 082180796X
Total Pages : 122 pages
Book Rating : 4.65/5 ( download)

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Download or read book Structurally Stable Quadratic Vector Fields written by Joan C. Artés and published by American Mathematical Soc.. This book was released on 1998 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 authors give all possible phase portraits for such structurally stable quadratic vector fields. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Joan C. Artés
Publisher : Springer Nature
ISBN 13 : 3030505707
Total Pages : 699 pages
Book Rating : 4.07/5 ( download)

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Download or read book Geometric Configurations of Singularities of Planar Polynomial Differential Systems written by Joan C. Artés and published by Springer Nature. This book was released on 2021-07-19 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 1461244269
Total Pages : 577 pages
Book Rating : 4.64/5 ( download)

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Download or read book Dynamics and Bifurcations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joan C. ArtŽs
Publisher : American Mathematical Soc.
ISBN 13 : 9780821863626
Total Pages : 124 pages
Book Rating : 4.22/5 ( download)

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Download or read book Structurally Stable Quadratic Vector Fields written by Joan C. ArtŽs and published by American Mathematical Soc.. This book was released on 1998-06-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Igor Gaissinski
Publisher : CRC Press
ISBN 13 : 1351029053
Total Pages : 495 pages
Book Rating : 4.56/5 ( download)

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Download or read book Modeling in Fluid Mechanics written by Igor Gaissinski and published by CRC Press. This book was released on 2018-06-13 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Takashi Matsumoto
Publisher : Springer Science & Business Media
ISBN 13 : 4431682430
Total Pages : 502 pages
Book Rating : 4.31/5 ( download)

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Download or read book Bifurcations written by Takashi Matsumoto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : M. Berz
Publisher : Soc for Industrial & Applied Math
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.73/5 ( download)

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Download or read book Computational Differentiation written by M. Berz and published by Soc for Industrial & Applied Math. This book was released on 1996 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author :
Publisher :
ISBN 13 :
Total Pages : 784 pages
Book Rating : 4.46/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Mike R. Jeffrey
Publisher : Springer
ISBN 13 : 3030021076
Total Pages : 521 pages
Book Rating : 4.78/5 ( download)

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Download or read book Hidden Dynamics written by Mike R. Jeffrey and published by Springer. This book was released on 2018-12-11 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes. Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down. In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.