Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control

We studied the dynamics of a prototypical electrochemical model, the electro- oxidation of hydrogen in the presence of poisons, under galvanostatic conditions. The lumped system exhibits relaxation oscillations, which develop mixed- mode oscillations ( MMOs ) for low preset currents. A fast- slow analysis of the homogeneous dynamics reveals that the MMOs arise from a fast oscillating subsystem and a one- dimensional slow manifold. In the spatially extended system, the galvanostatic constraint imposes a synchronizing global coupling that drives the system into cluster patterns. The properties of the cluster patterns ( CPs ) result from an intricate interplay of the nature of the local oscillators, the global constraint, and a nonlocal coupling through the electrolyte. In particular, we find that the global constraint suppresses small- amplitude oscillations of MMOs and prevents domains oscillating out of phase from occupying equal regions in phase space. The nonlocal coupling causes each individual clustered region to oscillate on a different limit cycle. Typically multistability of CPs is found. Coexisting patterns possess different oscillation periods and a different total fraction in space that occupies the in- phase or out- of- phase state, respectively. (C) 2008 American Institute of Physics.