Nonlinear Master Equation Approach to Asymmetrical Neural Networks of the Hopfield-Hemmen Type

Abstract

Dynamical properties of the Hopfield-Hemmen-type neural networks with asymmetrical synaptic connections are studied using a nonlinear master equation which is obtained in the thermodynamic limit from the Glauber dynamics assumed for the networks. A self-consistent equation is derived for the time evolution of the overlaps of the instantaneous configuration with the built-in patterns of a finite number p. Two fundamental types of conditions for the occurrence of limit cycle-type oscillation of the pattern overlaps are presented for the case of p=2.