Occurrence of Chaos and AT Line in Random Neural Networks.

By using a local-chaos hypothesis, we obtain the static mean-field equations giving the distribution for the fixed points of asymmetric random neural networks in the presence of an external field. These equations are the SK solutions for the Sherrington-Kirkpatrick model. We then study the critical value for the destabilization of the network, vs. the external field, and find it follows the De Almeida-Thouless line. We numerically compute the critical value for the entry into the chaotic regime and observe that, for increasing size, the destabilization line and the chaotic line collapse onto the AT line.