Quenched disorder and long-tail distributions

A model of overdamped and externally stimulated oscillators is discussed. It is shown analytically that in the uncoupled case a wide class of random distributions of parameters of individual oscillators leads to a long-tail distribution of resting points. Interactions between the individual oscillators destroy these long tails partially (nearest-neighbours interaction) or completely (mean field interactions). As the levels of a local coupling increase, domains of similarly acting oscillators are formed. The collective behaviour becomes important for large local coupling at which the long tails are destroyed. In this case, the observed pattern of resting states is a reflection of both the quenched disorder and interactions between the oscillators.