Pattern Formation in Globally Coupled Electrochemical Systems with an S-Shaped Current-Potential Curve
- Journal Article
The impact of global coupling on pattern formation in electrochemical systems with an S-shaped current potential curve is investigated theoretically and compared with the corresponding behavior in systems with N-shaped current potential characteristics. The global coupling, present under many experimental conditions, arises either owing to the galvanostatic operation mode or owing to the use of a Haber−Luggin capillary in a potentiostatic experiment. In the galvanostatic operation mode, any homogeneous current distribution of an S-NDR (S-type negative differential resistance) system is unstable in nearly the whole range of current values that lie on the NDR branch of the current potential curve. The system evolves either to a state composed of two stationary domains of low and high current density or to a more complicated stationary pattern with a larger wave number. The first attractor only exists in the presence of the global coupling, whereas the latter one is associated with a Turing-type instability and does not require the global constraint. In contrast, in N-NDR systems the galvanostatic control counteracts any pattern formation. The use of a Haber−Luggin capillary may stabilize stationary inhomogeneous structures only in N-NDR systems, but in both types of NDR systems it can induce pulses or standing waves with wavenumber 1. Furthermore, in S-NDR systems this bifurcation with a wavenumber 1 may compete or interact with the Turing-like bifurcation that dominates the spatiotemporal behavior in the absence of the global coupling. The interaction of these two bifurcations gives rise to a Turing−Hopf type codimension-2 bifurcation in in which two modes with nontrivial wavenumbers are involved. Show more
Journal / seriesThe Journal of Physical Chemistry B
Pages / Article No.
PublisherAmerican Chemical Society
Organisational unit09773 - Mazouz, Nadia / Mazouz, Nadia
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