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All solutions of a class of difference equations are truncated periodic. (English) Zbl 1029.39003
Author’s summary: 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 l0 such that (k-l)/2l+1) is a nonnegative even integer. The potential application of our results to neural networks is obvious.
MSC:
39A11Stability of difference equations (MSC2000)
92B20General theory of neural networks (mathematical biology)