Opinion evolution under mass media influence on the Barabasi–Albert network based on the q-voter model

In this paper, 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, [Formula: see text], at which the system consistently reaches complete consensus. This threshold probability [Formula: see text] decreases as the group size q increases, following a power-law relation [Formula: see text] with [Formula: see text]. 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 [Formula: see text], where [Formula: see text]. Conversely, an increase in the probability p results in a decrease in relaxation time following a power-law relationship [Formula: see text], with [Formula: see text]. The value of the exponent [Formula: see text] is similar to the exponents obtained in the voter and q-voter models across various network topologies.