Chaos in Random Neural Networks

A continuous-time dynamic model of a network of $N$ nonlinear elements interacting via random asymmetric couplings is studied. A self-consistent mean-field theory, exact in the $N\to \infty$ limit, predicts a transition from a stationary phase to a chaotic phase occurring at a critical value of the gain parameter. The autocorrelations of the chaotic flow as well as the maximal Lyapunov exponent are calculated.