Google matrix, dynamical attractors and Ulam networks

Details Google matrix, dynamical attractors and Ulam networks Google matrix, dynamical attractors and Ulam networks

2009-05-26

arxiv.org/abs/0905.4162v2

Phys. Rev. E v.81, p.036213 (2010)

Computer Science

Information Retrieval

9 pages, 11 figs; discussion, refs and fig added, data, title modified, research at http://www.quantware.ups-tlse.fr

Scientific paper

10.1103/PhysRevE.81.036213

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model creates the directed Ulam networks with approximate scale-free scaling and characteristics being rather similar to those of the World Wide Web. The simple dynamical attractors play here the role of popular web sites with a strong concentration of PageRank. A variation of the Google parameter $\alpha$ or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.

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