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Asymptotic Representation of Relaxation Oscillations in Lasers

  • Elena V. Grigorieva
  • Sergey A. Kaschenko

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Elena V. Grigorieva, Sergey A. Kaschenko
    Pages 1-25
  3. Elena V. Grigorieva, Sergey A. Kaschenko
    Pages 27-75
  4. Elena V. Grigorieva, Sergey A. Kaschenko
    Pages 77-127
  5. Elena V. Grigorieva, Sergey A. Kaschenko
    Pages 129-154
  6. Elena V. Grigorieva, Sergey A. Kaschenko
    Pages 155-186
  7. Back Matter
    Pages 187-230

About this book

Introduction

In this book we analyze  relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors.

 With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete   maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as  multistability of large-amplitude relaxation cycles, bifurcations of cycles,  controlled switching of regimes, phase synchronization  in an ensemble of coupled systems and others.

The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

Keywords

Laser dynamics relaxation oscillations mapping dynamics control optoelectronic feedback multistability

Authors and affiliations

  • Elena V. Grigorieva
    • 1
  • Sergey A. Kaschenko
    • 2
  1. 1.Department of MathematicsBelarus State Economical University Department of MathematicsMinskBelarus
  2. 2.Department of MathematicsYaroslavl State University Department of MathematicsYaroslavlRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42860-4
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-42859-8
  • Online ISBN 978-3-319-42860-4
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site