Rich dynamics and analog implementation of a Hopfield neural network in integer and fractional order domains

Abstract

Several synaptic weight matrices have been proposed for Hopfield neural network (HNN) models, where chaotic dynamics may arise. Contrary to those works, this manuscript aims to present a synaptic weight matrix where every entry can be set as an integer, harvesting an elegant chaotic HNN from a chaos theory point of view. Analytical and numerical analyses such as equilibrium points, bifurcation diagrams, Lyapunov exponents, and basins of attraction demonstrate that the proposed HNN exhibits complex behaviors across a wide range of parameter values. Also, we extend the study of the HNN into the fractional order domain. Moreover, the design and implementation details of the proposed neural network using field programmable analog arrays (FPAAs) are thoroughly discussed. This includes the various components and their configurations, highlighting how they contribute to the overall functionality of the neural network. As a result, we found a strong correlation between numerical simulations and SPICE circuit simulations.