Spatio-Temporal Chaos in the Complex Ginzburg-Landau Equation

There are three main regimes of complex dynamics in the complex Ginzburg-Landau equation:
  1. spatio-temporal intermittency
  2. amplitude chaos
  3. phase chaos.
The phase diagram for the one-dimensional case is shown below (H. Chate, Nonlinearity 7 (1994) 185).


Movies in the regime of amplitude chaos and phase chaos

A space-time diagram of the dynamics in the intermittent regime and a snapshot of a representative state are shown in the next two figures (H. Chate, Nonlinearity 7 (1994) 185).



Snapshots in the phase-chaotic and in the amplitude-chaotic regimes are shown below for the two-dimensional case.

Phasechaos: magnitude of the complex amplitude


This regime is characterized by the fact that no defects (i.e. points with vanishing oscillation amplitude appear).

Amplitude Chaos:real part of the complex amplitude and contour lines of real and imaginary part


The defects in the complex Ginzburg-Landau equation have the form of rotating spirals.