Symbolic walk in regular networks

LEONARDO ERMANN; GABRIEL G. CARLO

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Lugar: Londres; Año: 2014 vol. 48 p. 35102 - 35115

1751-8113

We find that a symbolic walk (SW)?performed by a walker with memorygiven by a Bernoulli shift?is able to distinguish between the random orchaotic topology of a given network. We show this result by means ofstudying the undirected baker network, which is defined by following theUlam approach for the baker transformation in order to introduce the effect ofdeterministic chaos into its structure. The chaotic topology is revealed throughthe central role played by the nodes associated with the positions corre-sponding to the shortest periodic orbits of the generating map. They are theoverwhelmingly most visited nodes in the limit cycles at which the SWasymptotically arrives. Our findings contribute to linking deterministic chaoticdynamics with the properties of networks constructed using the Ulamapproach.