Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associat...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 23; no. 2; pp. 335 - 342
Main Authors Luque, B., Ballesteros, F. J., Núñez, A. M., Robledo, A.
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.04.2013
Subjects
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
37E10
Quasiperiodicity
Complex networks
37E20
Circle map
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Summary:A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. Finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-012-9153-2