© 2017

Asymptotic Representation of Relaxation Oscillations in Lasers


  • This book presents an analytical method for description of stronly nonlinear relaxation pulsing in laser systems

  • As a result of asymptotic integration, the original differential system is reduced to a discrete mapping

  • The method is applied to systems of autonomous and non-autonomous ordinary differential equations, as well as to infinite-dimensional delay-differential systems and to partial differential equations in discrete form of coupled systems

  • By analyzing fixed points of the mapping, we conclude about the existence of pulse regimes and their bifurcations

  • By studying maps dynamics, we obtain the conditions for multi-rytmicity (coexistence of pulsings), quasiperiodic and chaotic pulsing

  • Describing the control method using a single short-time external impact to a laser system

  • Examples of controlled fast switching of pulse regimes, phase synchronization in an ensemble of coupled systems and others


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


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.


Laser dynamics relaxation oscillations mapping dynamics control optoelectronic feedback multistability

Authors and affiliations

  1. 1.Department of MathematicsBelarus State Economical University Department of MathematicsMinskBelarus
  2. 2.Department of MathematicsYaroslavl State University Department of MathematicsYaroslavlRussia

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