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.
Fractional Dynamics of Individuals in Complex Networks
Malgorzata Turalska and Bruce J. West
Front. Phys., 16 October 2018 | https://doi.org/10.3389/fphy.2018.00110