@ARTICLE{10.3389/fphy.2018.00110,
AUTHOR={Turalska, Malgorzata and West, Bruce J.},
TITLE={Fractional Dynamics of Individuals in Complex Networks},
JOURNAL={Frontiers in Physics},
VOLUME={6},
PAGES={110},
YEAR={2018},
URL={https://www.frontiersin.org/article/10.3389/fphy.2018.00110},
DOI={10.3389/fphy.2018.00110},
ISSN={2296-424X},
ABSTRACT={The relation between the behavior of a single element and the global dynamics of its host network is an open problem in the science of complex networks. We demonstrate that for a dynamic network that belongs 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.}
}