The effect of noise on the transition to chaos in random neural networks

Networks of randomly coupled rate neurons display a transition to chaos at a critical coupling strength (Sompolinsky et al. 1988, PRL). The dynamics close to the transition -- at the edge of chaos -- provides a powerful substrate for computations. Here, we investigate the effect of additive white noise, representing intrinsic stochasticity or external inputs, on the transition. We develop the dynamical mean-field theory yielding the autocorrelation function. Solving the eigenvalue problem for the maximum Lyapunov exponent allows us to analytically determine the transition from non-chaotic to chaotic activity. Increasing the noise amplitude shifts the transition to larger coupling strengths, i.e., chaos is suppressed. The decay time of the autocorrelation function does not diverge at the transition, but peaks slightly above the critical coupling strength. Partly supported by Helmholtz association: VH-NG-1028 and SMHB; EU Grant 604102 (HBP)