Trapping Electrochemical Oscillations between Self-Organized Potential Walls

Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling

A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.

Normal-form approach to spatiotemporal pattern formation in globally coupled electrochemical systems

We show that the experimental global coupling (GC) of spatially extended electrochemical oscillators is weak close to a supercritical Hopf bifurcation. A center manifold reduction allows then the normal form which comprises the GC and the naturally existing nonlocal (migration) coupling (NLC) to be derived. We show that 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.

A hierarchy of global coupling induced cluster patterns during the oscillatory H2-electrooxidation reaction on a Pt ring-electrode

We report experimental results on spatiotemporal pattern formation during the oscillatory hydrogen electrooxidation reaction on a Pt ring-electrode under negative (desynchronizing) global coupling (GC). Spatially one-dimensional profiles of the interfacial potential drop along the angular direction of the ring electrode are recorded by means of a potential probe. The dynamics is investigated as a function of two control parameters, the applied voltage U and the strength of the global coupling. The latter is adjusted either by varying the distance between the working electrode (WE) and the reference electrode (RE) or by inserting a negative impedance device in series with the WE. In the absence of global coupling, uniform oscillations were destabilized by migration coupling, and electrochemical turbulence developed at large values of U (H. Varela, C. Beta, A. Bonnefont and K. Krischer, Phys. Rev. Lett., 2005, 94, 174104; ). Already low global coupling strengths sufficed to suppress turbulence. Instead, regular two-phase clusters formed. At higher coupling strength, a second type of two-phase cluster was observed as well as two types of irregular cluster patterns, which were connected with an irregular motion of the cluster boundaries and the emergence and disappearance of clusters through splitting and merging of the boundaries, respectively. Upon increasing the coupling strength even further, five-phase clusters were stabilized and at the highest coupling strength applied the cluster patterns transformed into strongly modulated pulses. The two types of two-phase clusters and the five-phase clusters are analyzed employing several signal processing techniques.