Birkhäuser Advanced Texts Basler Lehrbücher

Introduction to the Qualitative Theory of Differential Systems

Planar, Symmetric and Continuous Piecewise Linear Systems

Authors: Llibre, Jaume, Teruel, Antonio E.

  • Excellent for learning the use of basic results on qualitative theory of differential systems
  • Illustrates how to use the Poincaré map for studying the periodic orbits of a differential system
  • Shows the importance of compactification of the domain of definition of a differential system for the understanding of the global dynamics of the system
  • Points out the importance of bifurcation diagrams for describing the different dynamics of differential systems depending on parameters
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eBook $59.99
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  • ISBN 978-3-0348-0657-2
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Hardcover $79.99
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  • ISBN 978-3-0348-0656-5
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  • Usually dispatched within 3 to 5 business days.
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About this Textbook

The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.

About the authors

Jaume Llibre is full professor at the Autonomous University of Barcelona (Spain) and a member of the Royal Academy of Sciences and Arts of Barcelona. He was a long-term visitor at different important universities and research institutes and is the author of many papers and some books. His main results deal with the periodic orbits either of different kinds of self-maps, or of vector fields, Hamiltonian systems and celestial mechanics. Antonio E. Teruel is associated professor at the University of the Balear Islands (Spain). He is the author of some papers about piecewise linear differential systems. His main results deal with piecewise linear models of differential behaviors.

Reviews

From the book reviews:

“This book is devoted to the study of piecewise linear differential systems (PWLSs), from the point of view of the qualitative theory of differential equations. … this book could serve well both as a textbook for a course in piecewise linear differential equations and as a reference in which important tools of current research are thoroughly explained and their use is illustrated.” (Claudio Pessoa, Mathematical Reviews, November, 2014)

“The monograph presents a detailed study of an important family of continuous piecewise linear differential systems. … The book is of great interest for researches working on planar piecewise linear differential systems. It can also serve as a reference book for those interested in the global phase portraits and the bifurcation sets of fundamental systems. The book is also highly suitable for students and engineers wishing to learn the theory of planar piecewise linear systems … .” (Valery Romanovski, zbMATH, Vol. 1286 (2), 2014)

Table of contents (5 chapters)

  • Introduction and Statement of the Main Results

    Llibre, Jaume (et al.)

    Pages 1-18

  • Basic Elements of the Qualitative Theory of Ordinary Differential Equations

    Llibre, Jaume (et al.)

    Pages 19-59

  • Fundamental Systems

    Llibre, Jaume (et al.)

    Pages 61-118

  • Return Maps

    Llibre, Jaume (et al.)

    Pages 119-187

  • Phase Portraits

    Llibre, Jaume (et al.)

    Pages 189-281

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-0348-0657-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-0348-0656-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to the Qualitative Theory of Differential Systems
Book Subtitle
Planar, Symmetric and Continuous Piecewise Linear Systems
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2014
Publisher
Springer Basel
Copyright Holder
Springer Basel
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-3-0348-0657-2
DOI
10.1007/978-3-0348-0657-2
Hardcover ISBN
978-3-0348-0656-5
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XIII, 289
Number of Illustrations and Tables
83 b/w illustrations, 1 illustrations in colour
Topics