Pattern Formation in Globally Coupled Electrochemical Systems with an S-Shaped Current-Potential Curve

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 ...