Delay-Coupled Complex Systems

and Applications to Lasers

  • Valentin Flunkert

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Stabilization of Odd-Number Orbits

    1. Front Matter
      Pages 1-1
    2. Valentin Flunkert
      Pages 3-6
    3. Valentin Flunkert
      Pages 7-10
    4. Valentin Flunkert
      Pages 11-25
    5. Valentin Flunkert
      Pages 27-34
    6. Valentin Flunkert
      Pages 45-53
    7. Valentin Flunkert
      Pages 55-66
    8. Valentin Flunkert
      Pages 67-85
  3. Synchronization of Delay Coupled Systems

    1. Front Matter
      Pages 87-87
    2. Valentin Flunkert
      Pages 89-91
    3. Valentin Flunkert
      Pages 111-119
    4. Valentin Flunkert
      Pages 121-135
    5. Valentin Flunkert
      Pages 137-147
    6. Valentin Flunkert
      Pages 149-150
  4. Appendix

    1. Front Matter
      Pages 151-151
    2. Valentin Flunkert
      Pages 153-163
    3. Valentin Flunkert
      Pages 165-178

About this book

Introduction

This thesis deals with the effects of time-delay in complex nonlinear systems and in particular with its applications in complex networks, and relates it to control theory and nonlinear optics. Delays arise naturally in networks of coupled systems due to finite signal propagation speeds and are thus a key issue in many areas of physics, biology, medicine, and technology. Synchronization phenomena in these networks play an important role, e.g., in the context of learning, cognitive and pathological states in the brain, for secure communication with chaotic lasers or gene regulation. The work includes both novel results on the control of complex dynamics by time-delayed feedback and new fundamental insights into the interplay of delay and synchronization. One of the most interesting results here is a solution to the problem of complete synchronization in general networks with large coupling delay, i.e., large distances between the nodes, by giving a universal classification of networks which has a wide range of interdisciplinary applications.

Keywords

Complex networks Control theory Delay coupling Non-linear optics Nonlinear dynamics Prizewinning thesis Secure communication Synchronization of Lasers Synchronization phenomena Time-delayed feedback

Authors and affiliations

  • Valentin Flunkert
    • 1
  1. 1., Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-20250-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-20249-0
  • Online ISBN 978-3-642-20250-6
  • About this book