Binary opinion dynamics with noise on random networks

Two kinds of noise strategies in binary opinion dynamics on ER random networks are discussed. Random noise p1 in the initial configuration plays a role in redistributing the opinion states associated with the network. Under synchronous updating, the system can attain a stable state within few time steps. The fraction of nodes with changed opinion states F decreases exponentially with time, and the ratio of one of the two opinion states R remains almost unchanged during the evolution. The average ratio <R> crosses at the half-half initial concentration under different p1. For noise in the dynamical evolution p2, the system can reach a steady state with small fluctuations. With larger p2, more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p2 is greater than 0.5, the two opinions coexist with equal support.