Motion in the space of memory patterns

The authors incorporate local threshold functions into the dynamics of the Hopfield model. These functions depend on the history of the individual neuron. Using functions that mimic fatigue of the single neuron, the authors turn the attractors of the usual model into transients, thus creating a dynamical system that moves around in pattern space, the space of all memories. They show that such motion has chaotic nature by studying a case of zero temperature in which the dynamics is completely deterministic. The authors investigate excitatory-inhibitory networks that are based on (0,1) elements and may be closer to neurological findings; they show that here too the thresholds lead to similar motion in pattern space. If the original memories have small overlaps with one another, the resulting motion follows along these implicit connections.