Statistical–Mechanical Analysis of Attractor Dynamics in a Hysteretic Neuron Network

Abstract

The attractor dynamics of a neural network of neurons with a hysteretic response property are investigated by a statistical–mechanical approach and numerical simulations using the Hopfield associative-memory model. Exact macroscopic flow equations for the case that the number of stored patterns is finite are derived, and the stability of attractors is evaluated. It is shown that the hysteretic property improves the robustness of both memory patterns and mixed states against temperature but does not affect the qualitative structure of the phase diagram. In addition, it is numerically showed that as the number of stored patterns increases and the state of the system becomes frustrated, the relaxation time becomes very long. In contrast to the results of the previous studies, however, memory capacity was not improved by the hysteretic property.