Desynchronization and clustering with pulse stimulations of coupled electrochemical relaxation oscillators

Effects of pulse stimulations on the dynamics of relaxation oscillator populations were experimentally studied in a globally coupled electrochemical system. Similar to smooth oscillations, weakly and moderately relaxational oscillations possess a vulnerable phase, ϕSϕS; pulses applied at ϕSϕS resulted in desynchronization followed by a return to the synchronized state. In contrast to smooth oscillators, weakly and moderately relaxational oscillators exhibited transient and itinerant cluster dynamics, respectively. With strongly relaxational oscillators the pulse applied at a vulnerable phase effected transitions to other cluster configurations without effective desynchronization. Repeated pulse administration resulted in a cluster state that is stable against the perturbation; the cluster configuration is specific to the pulse administered at the vulnerable phase. The pulse-induced transient clusters are interpreted with a phase model that includes first and second harmonics in the interaction function and exhibits saddle type cluster states with strongly stable intra-cluster and weakly unstable inter-cluster modes.