Fractional Stochastic Individuals

Abstract

The decision making model (DMM) [1,2] has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through size-dependent random fluctuations in the switching times between the two critical states of consensus. These properties are entailed by the fundamental assumption that the network elements in the DMM imperfectly imitate one another. The process of subordination establishes that a single network element can be described by a fractional master equation whose analytic solution yields the observed autocorrelation function obtained by numerical integration of the DMM to a high degree of accuracy.