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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Limit Cycle Structure for Block-Sequential Threshold Systems
verfasst von : Henning S. Mortveit
Erschienen in: Cellular Automata
Verlag: Springer Berlin Heidelberg
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This paper analyzes the possible limit set structures for the standard threshold block-sequential finite dynamical systems. As a special case of their work on Neural Networks (generalized threshold functions), Goles and Olivos (1981 [2]) showed that for the single block case (parallel update) one may only have fixed points and 2-cycles as
ω
-limit sets. Barrett et al (2006 [1]), but also Goles et al (1990 [3]) as a special case, proved that for the case with
n
blocks (sequential update) the only
ω
-limit sets are fixed points. This paper generalizes and unifies these results to standard threshold systems with block-sequential update schemes.