Noise dynamically suppresses chaos in random neural networks

Noise is ubiquitous in neural systems due to intrinsic stochasticity or external drive. For deterministic dynamics, randomly coupled neural networks display a transition to chaos at a critical coupling strength. Here, we investigate the effect of additive white noise on the onset of chaos. We develop the dynamical mean-field theory yielding the statistics of the activity and the maximum Lyapunov exponent. An exact condition determines the transition from stable to chaotic dynamics. Noise suppresses chaos by a dynamic mechanism, shifting the transition to significantly larger coupling strengths than predicted by local stability analysis. A regime emerges, where expansive dynamics and stable long-term behavior coexist. Furthermore, the time scale of the temporal correlations does not diverge at the transition, but peaks slightly above the critical coupling strength.