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Visibility graphs and symbolic dynamics. (arXiv:1704.06467v1 [nlin.CD])
来源于:arXiv
Visibility algorithms are a family of geometric and ordering criteria by
which a real-valued time series of N data is mapped into a graph of N nodes.
This graph has been shown to often inherit in its topology non-trivial
properties of the series structure, and can thus be seen as a combinatorial
representation of a dynamical system. Here we explore in some detail the
relation between visibility graphs and symbolic dynamics. To do that, we
consider the degree sequence of horizontal visibility graphs generated by the
one-parameter logistic map, for a range of values of the parameter for which
the map shows chaotic behaviour. Numerically, we observe that in the chaotic
region the block entropies of these sequences systematically converge to the
Lyapunov exponent of the system. Via Pesin identity, this in turn suggests that
these block entropies are converging to the Kolmogorov- Sinai entropy of the
map, which ultimately suggests that the algorithm is implicitly and adaptively
constructing 查看全文>>