Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Reaction-diffusion systems
DY 17.6: Vortrag
Mittwoch, 25. März 2009, 16:00–16:15, ZEU 118
Generalized Recurrence Quantification analysis reveals road to turbulence in the 2D Ginzburg-Landau equation — •Angelo Facchini1,2, Chiara Mocenni1,2, and Antonio Vicino1,2 — 1Center for the Study of Complex Systems, University of Siena, Italy — 2Department of Information Engineering, University of Siena, Italy
We use the Generalized Recurrence Plot (GRP) and the Generalized Recurrence Quantification Analysis (GRQA) (Phys. Lett. A, 360, 545, 2007) to investigate the pattern formed by the Complex Ginzburg-Landau Equation (CGLE)(Rev. Mod. Phys., 74, 99, 2002). The state of the dynamical system in steady state conditions is here represented by an image, and the application of the GRQA assign to each image a value for both ENT and DET (A. Facchini et al, Physica D (2008), in press). The signature of the dynamics of the CGLE is identified by the position of the image in the DET-ENT diagram. We focus on the portion of the parameter space in which there are both absolutely stable and unstable spiral wave solutions, separated by a bifurcation line (Physica A 224, 348, 1996). Our results show that images belonging to different stability zones are clustered in different regions of the DET-ENT diagram. By looking at the parameters value for which the position of the image jumps from a cluster to another we are able to reconstruct the bifurcation line in the DET-ENT diagram. Furthermore, before the onset of the turbulent state (cluster jump) we observe a transition region located along the reconstructed bifurcation line.