Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties
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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.
KeywordsQuasiperiodicity Complex networks Circle map
Mathematics Subject Classification37E10 37E20
B.L. and A.N. acknowledges support from FIS2009-13690 and S2009ESP-1691 (Spain); F.B. from AYA2006-14056, CSD2007-00060, and AYA2010-22111-C03-02 (Spain); A.R. from CONACyT & DGAPA (PAPIIT IN100311)-UNAM (Mexico).