A dynamic model for neural networks that explicitly takes into account the existence of several time scales without discretizing the time is studied analytically via the use of path integrals. The maximum capacity of the network is found to be that of the Hopfield model divided by 1+${\mathit{a}}^2$, with a the ratio of the refractory period to the action-potential duration. We obtain the phase diagram as a function of a, the capacity, and the temperature. The overall phase diagram is rich in structure, exhibiting first-order transitions as well as continuous ones.

• Received 4 September 1990

DOI:https://doi.org/10.1103/PhysRevA.43.1079