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Delay-Coupled Complex Systems

and Applications to Lasers

  • Book
  • © 2011

Overview

Authors:
  1. Valentin Flunkert

    1. , Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

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  • 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
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  2. Stabilization of Odd-Number Orbits

    1. Front Matter

      Pages 1-1
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  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. Towards Stabilization of Odd-Number Orbits in Experiments

      • Valentin Flunkert
      Pages 35-44

    6. Stabilization with Symmetric Feedback Matrices

      • Valentin Flunkert
      Pages 45-53

    7. Application to Laser Systems

      • Valentin Flunkert
      Pages 55-66

    8. Stabilization of Anti-Phase Orbits

      • Valentin Flunkert
      Pages 67-85

  4. Synchronization of Delay Coupled Systems

    1. Front Matter

      Pages 87-87
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  5. Synchronization of delay coupled systems

    1. Introduction

      • Valentin Flunkert
      Pages 89-91

    2. Structure of the Master Stability Function for Large Delay

      • Valentin Flunkert
      Pages 93-109

    3. Lang Kobayashi Laser Equations

      • Valentin Flunkert
      Pages 111-119

    4. Necessary Conditions for Synchronization of Lasers

      • Valentin Flunkert
      Pages 121-135

    5. Bubbling

      • Valentin Flunkert
      Pages 137-147

    6. Summary and Conclusions

      • Valentin Flunkert
      Pages 149-150

  6. Appendix

    1. Front Matter

      Pages 151-151
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    2. Delay Differential Equations

      • Valentin Flunkert
      Pages 153-163

    3. Pydelay: A Simulation Package

      • Valentin Flunkert
      Pages 165-178
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Keywords

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

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