Dynamics of Discrete Time, Continuous State Hopfield Networks

Abstract

The dynamics of discrete time, continuous state Hopfield networks is driven by an energy function. In this paper, we use this tool to prove under mild hypotheses that any trajectory converges to a fixed point for the sequential iteration, and to a cycle of length 2 or a fixed point for the parallel iteration. Perhaps surprisingly, it seems that no rigorous proof of these results was published before.