Lévy Flights, 1/f Noise and Self Organized Criticality

Oliver López Corona, Pablo Padilla, Oscar Escolero, Alejandro Frank, Ruben Fossion

IIMAS, Universidad Nacional Autónoma de México, Ciudad de México, México.
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad de México, México.
Instituto de Geología, Universidad Nacional Autónoma de México, Ciudad de México, México.
Instituto Nacional de Geratria, México.
Posgrado en Ciencias de la Tierra, Instituto de Geología, Universidad Nacional Autónoma de México, Ciudad de México, México.

DOI: 10.4236/jmp.2013.43046                

Abstract

A new analysis of a previously studied traveling agent model, showed that there is a relation between the degree of homogeneity of the medium where the agents move, agent motion patterns, and the noise generated from their displacements. We proved that for a particular value of homogeneity, the system self organizes in a state where the agents carry out Lévy walks and the displacement signal corresponds to 1/f noise. Using probabilistic arguments, we conjectured that 1/f noise is a fingerprint of a statistical phase transition, from randomness (disorder) to predictability (order), and that it emerges from the contextuality nature of the system which generates it.

Keywords

Lévy Flights; 1/f Noise; Self Organized Criticality; Agents Modelling; Complexity

Conflicts of Interest

The authors declare no conflicts of interest.

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