All solutions of a class of difference equations are truncated periodic Original Research Article

We propose the difference equation xn+1 = xn − f(xn−k) as a model for a single neuron with no internal decay, where f satisfies the McCulloch-Pitts nonlinearity. It is shown that every solution is truncated periodic with the minimal period 2(2l + 1) for some l ≥ 0 such that (k - l)/(2l + 1) is a nonnegative even integer. The potential application of our results to neural networks is obvious.