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 〈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.