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Chaos: Concepts, Control and Constructive Use

  • Yurii Bolotin
  • Anatoli Tur
  • Vladimir Yanovsky

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 1-3
  3. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 5-19
  4. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 21-44
  5. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 45-62
  6. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 63-109
  7. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 111-148
  8. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 149-173
  9. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 175-206
  10. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 207-243
  11. Yurii Bolotin, Anatoli Tur, Vladimir Yanovsky
    Pages 245-275
  12. Back Matter
    Pages 277-281

About this book

Introduction

This book offers a short and concise introduction to the many facets of chaos theory.

While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example.

The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others.

The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others.

This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently.

 

From the reviews of the first edition:

This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

Keywords

chaos control reconstruction of dynamical systems stochastic resonance synchronization in complex systems Quantum chaos Dynamical tunneling interfaces of quantum physics and dynamical systems quantum ratchets chaos as control parameter

Authors and affiliations

  • Yurii Bolotin
    • 1
  • Anatoli Tur
    • 2
  • Vladimir Yanovsky
    • 3
  1. 1.A.I. Akhiezer Institute for Theoretical PhysicsKharkovUkraine
  2. 2.Institut de Recherche en Astrophysique et PlanetologieCNRS Université Paul-SabatierToulouseFrance
  3. 3.National Academy of Sciences of UkraineInstitute for Single CrystalsKharkovUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42496-5
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-42495-8
  • Online ISBN 978-3-319-42496-5
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site
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