5 Summary

In this tutorial, the basic properties of the complex Ginzburg-Landau equation have been reviewed. The Ginzburg-Landau equation is important and worthwhile of study for two main reasons:

• It arises as the natural description of many physical situations, where a Hopf bifurcation is taking place in a continuous medium. Further, it is often the core component or 'kernel' of many other amplitude descriptions.
• Secondly, its solutions display a rich and exotic spectrum of behaviours, reflecting the interplay of dissipation, dispersion and nonlinearity. A large family of coherent structures are admitted as solutions and it is an ideal equation for the study of various aspects of spatiotemporal chaos

This tutorial has only scratched the surface of the body of work available concerning the CGLE. The interested reader is encouraged to pursue the references listed in the next section, in particular, the general review of Aranson and Kramer (2002). Also, the complicated patterns and behaviours detailed here can easily be reproduced and examined by downloading the MATLAB code from the resources page.

The study of the CGLE over the last few decades have had an enormous impact on the study of non-equilibrium systems. The insights gained from this analysis should be invaluable to future progress in the study of complex systems.