Effect of network topology on the controllability of voter model dynamics using biased nodes

This paper examines the effects of biased nodes on the voter model dynamics where each node is characterized by binary states s_i = ±1. For a fully connected graph, the master equation is shown to have the form of the Fokker-Planck equation, and necessary and sufficient conditions for the existence of a polynomial solution are investigated. Numerical simulations and analytical results are studied for a complete graph and the Erdös-Rényi network to reveal several interesting characteristics of the dynamical system. One of the key findings is that the equilibrium probability density of the network can be controlled by selecting the size of the influence groups. Population size, relative size of the biased groups, initial conditions and network parameters such as connection probabilities are discussed and their effects on the equilibrium probability density and time to convergence are investigated and reported.