Physics – Condensed Matter
Scientific paper
1995-08-25
Physica D 96 47-65 (1996).
Physics
Condensed Matter
20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nepg
Scientific paper
We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.
Hernandez-Garcia Emilio
Miguel Maxi San
Montagne Raul
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