Complex dynamics in simple neural circuits

Abstract

Simple circuits incorporating one or two electronic ‘neurons’ are shown to be capable of complex nonlinear behavior. Underdamped transients and instability leading to oscillation are possible when the neurons possess a finite frequency response or a delay in their transfer characteristic. Inertial terms in the dynamics allow intertwined basins of attraction and chaotic response to an external drive. These phenomena constrast with the steady state asymptotic behavior and overdamped transients exhibited by Hopfield’s deterministic model with symmetric RC couplings, and indicate that care should be exercised when adding inertia to enhance performance of optimizing networks or when implementing networks electronically.