Pattern formation in globally coupled electrochemical systems with an S-Shaped current-potential curve

The impact of global coupling on pattern formation in electrochemical syste ms with an S-shaped current potential curve is investigated theoretically a nd compared with the corresponding behavior in systems with N-shaped curren t potential characteristics. The global coupling, present under many experi mental conditions, arises either owing to the galvanostatic operation mode or owing to the use of a Haber-Luggin capillary in a potentiostatic experim ent. In the galvanostatic operation mode, any homogeneous current distribut ion of an S-NDR (S-type negative differential resistance) system is unstabl e 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 com plicated 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 globa l constraint. In contrast, in N-NDR systems the galvanostatic control count eracts any pattern formation. The use of a Haber-Luggin capillary may stabi lize stationary inhomogeneous structures only in N-NDR systems, but in both types of NDR systems it can induce pulses or standing waves with wavenumbe r 1. Furthermore, in S-NDR systems this bifurcation with a wavenumber 1 may compete or interact with the Turing-like bifurcation that dominates the sp atiotemporal behavior in the absence of the global coupling. The interactio n of these two bifurcations gives rise to a Turing-Hopf type codimension-2 bifurcation in in which two modes with nontrivial wavenumbers are involved.