Delay-induced spatial correlations in one-dimensional stochastic networks with nearest-neighbor coupling.

We consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time-delayed feedback. (i) For a deterministic system, we study propagation of waves through the network. We show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities, which we compute analytically. (ii) For noisy system, we study the response of the network to external random forcing correlated in space and uncorrelated in time. Below the threshold of spatial instability, noise induces spatiotemporal fluctuations, which can be characterized by the structure function. We give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode.