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Zbl 1029.39003
Chen, Yuming
All solutions of a class of difference equations are truncated periodic. (English)
[J] Appl. Math. Lett. 15, No.8, 975-979 (2002). ISSN 0893-9659

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 $l\geq 0$ such that $(k-l)/2l+1)$ is a nonnegative even integer. The potential application of our results to neural networks is obvious.
[Mihaly Pituk (Veszprem)]

MSC 2000:: *39A11 Stability of difference equations
92B20 General theory of neural networks

Keywords: difference equation; truncated periodic solution; neural network; McCulloch-Pitts nonlinearity

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