Chaotic Behavior for Asymmetrically Diluted Hopfield Neural Network with a Non-Monotonic Transfer Function

Abstract

We investigate retrieval properties for a synchronous asymmetrically diluted Hopfield neural network with a non-monotonic transfer function by an analytic method. Because of asymmetry of interaction and non-monotonicity of the transfer function, it is difficult to use conventional methods of the equilibrium statistical mechanics in order to investigate the network. We therefore use a generating-function method of path-integral representation, and then obtain an equation for a dynamical order parameter. We find chaotic behavior for the retrieval overlap by choosing a threshold adequately; a Lyapunov exponent is positive in that case. We clarify a bifurcation diagram in a plane specified by a threshold and a load parameter at zero temperature.