Chapter 5. Topological Defects and Control of Spatio-Temporal Chaos

  1. Heinz G. Schuster
  1. I. Aranson

Published Online: 31 MAY 2006

DOI: 10.1002/3527607455.ch5

Handbook of Chaos Control

Handbook of Chaos Control

How to Cite

Aranson, I. (1999) Topological Defects and Control of Spatio-Temporal Chaos, in Handbook of Chaos Control (ed H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527607455.ch5

Editor Information

  1. University of Kiel, Institute of Theoretical Physics, Leibnizstr. 15, D-24098 Kiel, Germany

Author Information

  1. Material Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne,IL 60439, France

Publication History

  1. Published Online: 31 MAY 2006
  2. Published Print: 23 FEB 1999

ISBN Information

Print ISBN: 9783527294367

Online ISBN: 9783527607457



  • topological defects;
  • control of spatiotemporal chaos;
  • Ginzburg-Landau equation;
  • plane waves;
  • instability of traveling waves;
  • hole solution;
  • reaction-diffusion systems


This chapter contains sections titled:

  • Introduction

  • Complex Ginzburg-Landau equation and its basic solutions

  • Stability of Basic Solutions

    • Stability of plane waves

    • Absolute versus Convective Instability of Traveling Waves

    • Stability of topological defects in one and two dimensions

  • Control of Chaos in the Complex Ginzburg-Landau Equation

    • One-dimensional situation. Control of the hole solution

    • Control of spiral in the two-dimensional complex complex Ginzburg-Landau Equation

  • Control of Spatio-Temporal Chaos in Reaction-Diffusion Systems

  • Conclusion