Topologically determined optimal stochastic resonance responses of spatially embedded networks

Abstract

We have analyzed the stochastic resonance phenomenon on spatial networks of bistable and excitable oscillators, which are connected according to their location and the amplitude of external forcing. By smoothly altering the network topology from a scale-free (SF) network with dominating longrange connections to a network where principally only adjacent oscillators are connected, we reveal that besides an optimal noise intensity, there is also a most favorable interaction topology at which the best correlation between the response of the network and the imposed weak external forcing is achieved. For various distributions of the amplitudes of external forcing, the optimal topology is always found in the intermediate regime between the highly heterogeneous SF network and the strong geometric regime. Our findings thus indicate that a suitable number of hubs and with that an optimal ratio between short-and long-range connections is necessary in order to obtain the best global response of a spatial network. Furthermore, we link the existence of the optimal interaction topology to a critical point indicating the transition from a long-range interactionsdominated network to a more lattice-like network structure. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.