Física estatística dos sistemas complexos : aplicações interdisciplinares

Abstract

In the present work, we apply concepts and methods from statistical physics to study complex systems. Specifically, we analyze the dynamics of i) circulation of magazines; ii) citations to scientific journals; iii) religious activities of Jehovah's Witnesses; and iv) a geomagnetic signal - the Dst index. In all the cases we find evidence of scaling behavior and universality. For the systems i, ii and iii, we show that: 1) the distribution of sizes exhibits power law asymptotic behavior; 2) the distribution of growth rates displays a universal form which does not depend on the size or on the measure of size used; 3) the standard deviation of growth rates decays with size as a power law; 4) these findings are remarkably similar to those observed in the dynamics of economic and scientific research activities. Furthermore, we propose two stochastic models in order to reproduce distinct aspects of the observed behavior. Moreover, for the system iv, we show that: 1) the distribution of Dst increments exhibits the same functional form for a wide range of time scales, presenting power law asymptotic behavior; 2) Dst series are long-range correlated, being well approximated by a 1/f noise; 3) magnitude series of Dst increments are long-range correlated (persistent behavior); 4) sign series of Dst increments are long-range anti-correlated (anti-persistent behavior); 5) Dst series present multifractal properties; 6) periods of high and low geomagnetic activity exhibit similar multifractal properties; 7) these findings are surprisingly similar to those observed in the dynamics of a physiologic signal. In general, our findings may contribute to a better understanding of the mechanisms which govern the dynamics of the systems considered, serving as a guide to develop models reproducing the observed behavior .