A Unified Tractable Approach for Random Drifts on Dynamical Networks

This brief proposes a novel approach to exploring random drift processes on complex dynamical networks. This approach uses characteristics of the influence model in order to provide a unified analytically tractable framework for analysis of random drift on networks. Based on this approach, the fixation probability, which is a key quantity characterizing random drift, is obtained for three kinds of state-updating dynamics, including the birth-death, death-birth, and link selection updating rules for the first time. The results lay out a clear understanding on how the dynamical structure affects the fixation of mutant on networks under random drift.