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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ramacos Fardela & Zulfi Abdullah & Roni Muslim, 2025. "Opinion evolution under mass media influence on the Barabasi–Albert network based on the q-voter model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-13, April.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:04:n:s0129183124502115
    DOI: 10.1142/S0129183124502115
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