Discrete Chaos *
نویسندگان
چکیده
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ω = (B ∞ , T ∆). These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology T ∆ which we call a semicausal topology. We show that Ω is a metrizable Cantor set which embeds the chaotic attractor Λ. We discuss metrical properties, including the correlation dimension of Λ. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with " memory " , on the other hand, does appear to be an example of discrete chaos.
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