Associative memory in a circular neural network

We study the dynamics of recalling of a random bit sequence in a circular neural network of Hopfield type. In the continuum limit ($N\to\infty$), the evolution equation in terms of an overlap function is derived provided a finite number $p$ of informational copies (“replicas”). Two stationary regimes: a spontaneous information retrieval and that governed by external input signal, both of travelling-wave type, are studied by solving the evolution equation and by numerical experiments as well. The domains in which robust functioning of the system as an associative memory is possible are determined in numerical simulations.