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 p (1) 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 aOE (c) R > crosses at the half-half initial concentration under different p (1). For noise in the dynamical evolution p (2), the system can reach a steady state with small fluctuations. With larger p (2), more nodes have changed opinion states at each updating and more nodes with opposite opinions coexist. If p (2) is greater than 0.5, the two opinions coexist with equal support.