Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Reaction-diffusion systems

DY 17.5: Talk

Wednesday, March 25, 2009, 15:45–16:00, ZEU 118

Extended complex Ginzburg-Landau equation for globally coupled electrochemical systems — •Vladimir Garcia-Morales and Katharina Krischer — Technische Universität München, Physik Department E19, James-Franck Str. 1, D-85748 Garching bei München, Germany

Nonlocal interactions in spatially extended electrochemical oscillators arise because of the effect of inhomogeneities in the distribution of the electrostatic potential. We have derived a nonlocal complex Ginzburg-Landau equation (NCGLE) that accounts for this nonlocal coupling (NLC) at the vicinity of a supercritical Hopf bifurcation.

Experimentally, it is straightforward to add a global coupling (GC) to the nonlocally coupled electrochemical oscillators. GC occurs naturally in these systems, for example, when an external resistance is introduced or when part of the cell resistance is compensated, an often applied technique in electrochemical experiments.

In this talk we discuss how the NCGLE can be extended rigorously to account for the GC of electrochemical oscillators. We show that the experimental GC is also weak close to the supercritical Hopf bifurcation, having the same scaling properties as the NLC. Therefore, a center manifold reduction allows the NCGLE to be extended rigorously to account for the GC. We discuss how the interaction between NLC and GC widens the spectrum of coherent structures found in globally coupled oscillatory media and allows for wavelength selection of standing waves, stabilization of phase clusters without breaking phase invariance, and creation of heteroclinic networks connecting families of oscillatory states characterized by different spatial symmetries.