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

Abstract

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.

Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media

“…In a cluster state, the system separates into distinct regions with mutual phase shifts. In several experimental setups a global coupling arises naturally or can be implemented easily and thus, cluster formation has been observed in various systems [2][3][4][5][6] .…”

Pattern formation during the oscillatory photoelectrodissolution of n-type silicon: turbulence, clusters and chimeras

“…This applies, e.g., to electrically controlled systems, such as semiconductor devices [11,12], gas discharge tubes [13] or electrochemical systems [14][15][16][17]. The most prominent patterns emerging from a global coupling are scale free cluster patterns where the medium separates into a few domains, oscillating with a certain, constant phase lag [18][19][20][21][22].…”

Two-cluster solutions in an ensemble of generic limit-cycle oscillators with periodic self-forcing via the mean-field

“…They have been described in Refs. [9][10][11][12]. In this state the clusters are a modulation of a homogeneous oscillation, as visible in Fig.…”

“…Similar states were observed in continuous systems in Refs. [5,[9][10][11][12]21]. In the amplitude cluster state the two groups oscillate on different limit cycles separated by an amplitude difference, while the phase shift is much smaller than π [19].…”

“…In many cases the amplitude variations in these states are very small and the dynamics can be approximated by phase models. However, as one prominent counter example, we present a type of clusters, so-called type II clusters [9], where essential variations in the amplitudes occur. They have been described in Refs.…”