Fractional Dynamics of Individuals in Complex Networks

Frontiers in Physics

Turalska, Malgorzata¹  West, Bruce J.² 

[1] Computational and Information Sciences Directorate, US Army Research Laboratory, United States;Information Sciences Directorate, US Army Research Office, United States

关键词: fractional calculus;    subordination;    inverse power law;    complex networks;    Control;   

DOI  :  10.3389/fphy.2018.00110

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

The dependence of the behavior of a single individual on the global dynamics of the social network to which it belongs is an open problem in sociology. We demonstrate that for a dynamical network belonging to the Ising universality class this problem can be approached analytically through a subordination procedure. The analysis leads to a linear fractional differential equation of motion for the average trajectory of the individual, whose analytic solution for the probability of changing states is a Mittag-Leffler function. Consequently, the analysis provides a linear description of the average dynamics of an individual, without linearization of the complex network dynamics.

【 授权许可】

CC BY