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Bifurcations in Continuous Piecewise Linear Differential Systems, Ponce


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Автор: Ponce
Название:  Bifurcations in Continuous Piecewise Linear Differential Systems
ISBN: 9783031211348
Издательство: Springer
Классификация:

ISBN-10: 3031211340
Обложка/Формат: Hardback
Страницы: 311
Вес: 0.72 кг.
Дата издания: 25.12.2022
Серия: RSME Springer Series
Язык: English
Издание: 1st ed. 2022
Иллюстрации: 1 illustrations, black and white; xv, 311 p. 1 illus.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: Applications to low-dimensional electronic oscillators
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and presenting two or three regions of linearity. The study focuses on the more common bifurcations that PWL differential systems can undergo, with emphasis on those leading to limit cycles. Similarities and differences with respect to their smooth counterparts are considered and highlighted. Regarding the dimensionality of the addressed problems, some general results in arbitrary dimensions are included. The manuscript mainly addresses specific aspects in PWL differential systems of dimensions 2 and 3, which are sufficinet for the analysis of basic electronic oscillators. The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits. The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices. In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.
Дополнительное описание: - Part I Introduction. - 1. From Linear to Piecewise Linear Differential Systems. - 2. Preliminary Results. - Part II Planar Piecewise Linear Differential Systems. - 3. Analysis of Planar Continuous Systems with Two Zones. - 4. First Results for Planar Co



Introduction to the Qualitative Theory of Differential Systems

Автор: Jaume Llibre; Antonio E. Teruel
Название: Introduction to the Qualitative Theory of Differential Systems
ISBN: 3034806566 ISBN-13(EAN): 9783034806565
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This book introduces the basic tools of the qualitative theory of ordinary differential equations. It is ideal for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

Автор: Gelfgat
Название: Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics
ISBN: 3319914936 ISBN-13(EAN): 9783319914930
Издательство: Springer
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Цена: 20962.00 р.
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Описание: Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years.

Dynamic Bifurcations

Автор: Eric Benoit
Название: Dynamic Bifurcations
ISBN: 3540549005 ISBN-13(EAN): 9783540549000
Издательство: Springer
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Цена: 4884.00 р.
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Описание: Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems, when the parameter is a slowly varying function of time. This book offers an introduction to this topic.

Generating Families in the Restricted Three-Body Problem

Автор: Michel Henon
Название: Generating Families in the Restricted Three-Body Problem
ISBN: 3540417338 ISBN-13(EAN): 9783540417330
Издательство: Springer
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Цена: 19564.00 р.
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Описание: The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. This book is interested in the restricted problem and its applications to astronomy.

Normal Forms, Bifurcations and Finiteness Problems in Differential Equations

Автор: Gert Sabidussi; Yulij Ilyashenko; Christiane Rouss
Название: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations
ISBN: 1402019289 ISBN-13(EAN): 9781402019289
Издательство: Springer
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Цена: 33401.00 р.
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Описание: Presents many significant developments in the theory of differential equations. This book covers subjects, such as: tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, and more.

Normal Forms, Bifurcations and Finiteness Problems in Differential Equations

Автор: Gert Sabidussi; Yulij Ilyashenko; Christiane Rouss
Название: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations
ISBN: 1402019297 ISBN-13(EAN): 9781402019296
Издательство: Springer
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Цена: 21661.00 р.
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Описание: Presents significant developments in the theory of differential equations. The following subjects are covered: tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, and more.

Continuation and Bifurcations: Numerical Techniques and Applications

Автор: Dirk Roose; Bart De Dier; Alastair Spence
Название: Continuation and Bifurcations: Numerical Techniques and Applications
ISBN: 9401067813 ISBN-13(EAN): 9789401067812
Издательство: Springer
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Цена: 12157.00 р.
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Описание: Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Автор: Guckenheimer John, Holmes Philip
Название: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
ISBN: 0387908196 ISBN-13(EAN): 9780387908199
Издательство: Springer
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Цена: 18167.00 р.
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Описание: From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Dynamics and Bifurcations

Автор: Jack K. Hale; H. Buttanri; H?seyin Kocak
Название: Dynamics and Bifurcations
ISBN: 1461287650 ISBN-13(EAN): 9781461287650
Издательство: Springer
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Цена: 11313.00 р.
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Описание: 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.

Bifurcations and Periodic Orbits of Vector Fields

Автор: Dana Schlomiuk
Название: Bifurcations and Periodic Orbits of Vector Fields
ISBN: 0792323920 ISBN-13(EAN): 9780792323921
Издательство: Springer
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Цена: 46399.00 р.
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Описание: 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.

Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics

Автор: Alexander Gelfgat
Название: Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics
ISBN: 3030082601 ISBN-13(EAN): 9783030082604
Издательство: Springer
Рейтинг:
Цена: 20962.00 р.
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Описание: Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

Generating Families in the Restricted Three-Body Problem

Автор: Michel Henon
Название: Generating Families in the Restricted Three-Body Problem
ISBN: 3662145170 ISBN-13(EAN): 9783662145173
Издательство: Springer
Рейтинг:
Цена: 13060.00 р.
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