All solutions of a class of difference equations are truncated periodic

We propose the difference equation (x)n+1 = x(n) - f(x(n-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 greater than or equal to 0 such that (k - l)/(2l + 1) is a nonnegative even integer. The potential application of our results to neural networks is obvious. (C) 2002 Elsevier Science Ltd. All rights reserved.