Opinion formation under mass media influence on the Barabasi-Albert network

We study numerically the dynamics of opinion formation under the influence of mass media using the q-voter model on a Barabasi-Albert network. We investigate the scenario where a voter adopts the mass media's opinion with a probability p when there is no unanimity among a group of q agents. Through numerical simulation, we identify a critical probability threshold, pₜ, at which the system consistently reaches complete consensus. This threshold probability pₜ decreases as the group size q increases, following a power-law relation pₜ ∝ qγ with γ ≈ -1.187. Additionally, we analyze the system's relaxation time, the time required to reach a complete consensus state. This relaxation time increases with the population size N, following a power-law τ ∝ Nν, where ν ≈ 1.093. Conversely, an increase in the probability p results in a decrease in relaxation time following a power-law relationship τ ∝ pδ, with δ ≈ -0.596. The value of the exponent \( ν \) is similar to the exponents obtained in the voter and q-voter models across various network topologies.