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  • Book
  • © 2011

Delay-Coupled Complex Systems

and Applications to Lasers

Authors:

  • Reports important progress in the control of complex dynamics
  • Gives fundamental insights into the interplay of delay and synchronization
  • Nominated as an outstanding contribution by the Technical University of Berlin

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiii
  2. Stabilization of Odd-Number Orbits

    1. Front Matter

      Pages 1-1
  3. Stabilization of odd-number orbits

    1. Introduction

      • Valentin Flunkert
      Pages 3-6
    2. Time-Delayed Feedback Control

      • Valentin Flunkert
      Pages 7-10
    3. Counterexample

      • Valentin Flunkert
      Pages 11-25
    4. Odd-Number Orbits Close to a Fold Bifurcation

      • Valentin Flunkert
      Pages 27-34
    5. Stabilization with Symmetric Feedback Matrices

      • Valentin Flunkert
      Pages 45-53
    6. Application to Laser Systems

      • Valentin Flunkert
      Pages 55-66
    7. Stabilization of Anti-Phase Orbits

      • Valentin Flunkert
      Pages 67-85
  4. Synchronization of Delay Coupled Systems

    1. Front Matter

      Pages 87-87
  5. Synchronization of delay coupled systems

    1. Introduction

      • Valentin Flunkert
      Pages 89-91
    2. Lang Kobayashi Laser Equations

      • Valentin Flunkert
      Pages 111-119
    3. Necessary Conditions for Synchronization of Lasers

      • Valentin Flunkert
      Pages 121-135
    4. Bubbling

      • Valentin Flunkert
      Pages 137-147
    5. Summary and Conclusions

      • Valentin Flunkert
      Pages 149-150
  6. Appendix

    1. Front Matter

      Pages 151-151
    2. Delay Differential Equations

      • Valentin Flunkert
      Pages 153-163
    3. Pydelay: A Simulation Package

      • Valentin Flunkert
      Pages 165-178

About this book

This work addresses time-delay in complex nonlinear systems and, in particular, its applications in complex networks; its role in control theory and nonlinear optics are also investigated. 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 for gene regulation. The thesis includes both novel results on the control of complex dynamics by time-delayed feedback and fundamental new 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 that has a wide range of interdisciplinary applications.

Authors and Affiliations

  • , Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Valentin Flunkert

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access