Noise enhanced signal correlation and wave propagation in networks of oscillatory and excitable systems

Processes in coupled nonlinear systems are discussed under the influence of external signals and noise to improve the understanding of dynamical order and function in biological systems. A network of relaxation-type oscillators with nearest-neighbour coupling is numerically investigated under the influence of exponentially correlated noise. When all oscillators are exposed to an aperiodic subthreshold signal and to spatially incoherent noise, two regimes of behaviour are observed depending on the network's coupling strength. In the case of weak coupling, noise at an intermediate level optimizes the correlation of the network oscillators with the aperiodic signal. In the case of stronger coupling the correlation with the external signal becomes lost, as intrinsic network dynamics take over. When the network is locally excited, noise-induced plane waves are built up, which move through the entire system. It is shown that the spatio-temporal pattern emerges independently of the way of the deterministic forcing. This effect may be understood as spatio-temporal stochastic resonance, since noise of an intermediate level optimizes the coherence of the wave-fronts.