Order-parameter flow in symmetric and nonsymmetric fully connected attractor neural networks near saturation

We apply a recent theory by Coolen and Sherrington [Phys. Rev. E. 49, 1921 (1994)] which describes the dynamics of the Hopfield model near saturation in terms of deterministic flow equations for order parameters to the more general and technically more complicated case of neural networks with (i) arbitrary separable interactions, which (ii) need not be symmetric, and with (iii) more than one condensed pattern. Following the key assumptions of the previous theory, the distribution of intrinsic noise components of the alignment fields is calculated with the replica method. In the region where replica symmetry is stable, numerical simulations show that our equations capture the essential features of the flow, even for nonsymmetric systems (i.e., without detailed balance). For symmetric systems, the fixed points of the flow are shown to reproduce the thermodynamic equilibrium equations recently obtained by Cugliandolo and Tsodyks [J. Phys. A 27, 741 (1994)].