Google matrix and dynamical attractors

Dima Shepelyansky (1) , O. V. Zhirov (2)

1 ICQ - Cohérence Quantique (LPT)
2 BINP - Budker Institute of Nuclear Physics

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. This simple dynamical model creates scale-free directed networks with 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 system parameters drives the system to a delocalized phase with a strange attractor where the Google search becomes inefficient.

Mots clés: Google strange attractor

Domaines: Recherche d'information [cs.IR]

Dima Shepelyansky, O. V. Zhirov. Google matrix and dynamical attractors. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2010, 81, pp.036213. ⟨10.1103/PhysRevE.81.036213⟩. ⟨hal-00388656⟩