Atlantis Studies in Mathematics for Engineering and Science

Nonlinear Hybrid Continuous/Discrete-Time Models

Authors: Akhmet, Marat

  • Most general differential equations with piece-wise constant argument are investigated
  • New technique of analysis is used. A new model of blood pressure distribution is introduced with complete analysis Synchronization of quite identical integrate-and-fire oscillators is proved
  • General model of quite identical integrate-and-fire oscillators is constructed
  • Model of recurrent neural networks with continuous/discrete-time is investigated
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eBook $109.00
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  • ISBN 978-94-91216-03-9
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Hardcover $139.00
price for USA
  • ISBN 978-94-91216-02-2
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  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-94-91216-38-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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About this book

The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.

Reviews

From the reviews:

“Hybrid systems are a recent concept in dynamical systems theory and have important and extensive applications. … The present book generalizes the concept of differential equations with piecewise constant argument by considering a more general type of equations and develops new methodological approaches to explore those challenging systems. … This book is well written and readable and will be extremely useful not only to expert readers but also to graduate and advanced undergraduate students.” (Meng Fan, Mathematical Reviews, January, 2013)


Table of contents (10 chapters)

  • Introduction

    Akhmet, Marat

    Pages 1-15

  • Linear and Quasi-Linear Systems with Piecewise Constant Argument

    Akhmet, Marat

    Pages 17-32

  • The Reduction Principle for Systems with Piecewise Constant Argument

    Akhmet, Marat

    Pages 33-48

  • The Small Parameter and Differential Equations with Piecewise Constant Argument

    Akhmet, Marat

    Pages 49-69

  • Stability

    Akhmet, Marat

    Pages 71-88

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-91216-03-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-94-91216-02-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-94-91216-38-1
  • 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
Nonlinear Hybrid Continuous/Discrete-Time Models
Authors
Series Title
Atlantis Studies in Mathematics for Engineering and Science
Series Volume
8
Copyright
2011
Publisher
Atlantis Press
Copyright Holder
Atlantis Press
eBook ISBN
978-94-91216-03-9
DOI
10.2991/978-94-91216-03-9
Hardcover ISBN
978-94-91216-02-2
Softcover ISBN
978-94-91216-38-1
Series ISSN
1875-7642
Edition Number
1
Number of Pages
XIII, 216
Topics