Dynamics of Nonlinear Time-Delay Systems

  • Muthusamy Lakshmanan
  • Dharmapuri Vijayan Senthilkumar

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. M. Lakshmanan, D.V. Senthilkumar
    Pages 1-15
  3. M. Lakshmanan, D.V. Senthilkumar
    Pages 17-29
  4. M. Lakshmanan, D.V. Senthilkumar
    Pages 55-84
  5. M. Lakshmanan, D.V. Senthilkumar
    Pages 85-103
  6. M. Lakshmanan, D.V. Senthilkumar
    Pages 165-199
  7. M. Lakshmanan, D.V. Senthilkumar
    Pages 201-226
  8. M. Lakshmanan, D.V. Senthilkumar
    Pages 227-250
  9. M. Lakshmanan, D.V. Senthilkumar
    Pages 251-258
  10. Back Matter
    Pages 259-313

About this book

Introduction


Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths
of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant.

This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics.
Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions.


Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.

Keywords

chaotic dynamical systems delay differential equations delay feedback electronic circuits in complex networks recurrence plots and analysis synchronization time delay systesm

Authors and affiliations

  • Muthusamy Lakshmanan
    • 1
  • Dharmapuri Vijayan Senthilkumar
    • 2
  1. 1.Centre for Nonlinear DynamicsTiruchirapalliIndia
  2. 2.Research Domain IV, Transdisciplinary Concepts and MethodsPotsdam Institute for Climate Impact ResPotsdamGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14938-2
  • Copyright Information Springer Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-14937-5
  • Online ISBN 978-3-642-14938-2
  • Series Print ISSN 0172-7389
  • About this book