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

Ramacos Fardela, Zulfi Abdullah () and Roni Muslim ()
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Ramacos Fardela: Department of Physics, Universitas Andalas, Padang, Limau Manis 25163, Indonesia
Zulfi Abdullah: Theoretical Physics Laboratory, Department of Physics, Universitas Andalas, Padang, Limau Manis 25163, Indonesia
Roni Muslim: Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 04, 1-13

Abstract: 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, 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.

Keywords: Sociophysics; q-voter model; agent-based model; mass media influence; consensus (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124502115

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