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Ordering dynamics in the voter model with aging

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  • Peralta, Antonio F.
  • Khalil, Nagi
  • Toral, Raúl

Abstract

We study theoretically and numerically the voter model with memory-dependent dynamics at the mean-field level. The “internal age”, related to the time an individual spends holding the same state, is added to the set of binary states of the population, such that the activation probability pi for attempting a change of state has an explicit dependence on the internal age i. We derive a closed set of integro-differential equations describing the time evolution of the fraction of individuals with a given state and internal age, and from it we obtain analytical results characterizing the behavior of the system close to the absorbing states. In general, different internal age-dependent activation probabilities pi have different effects on the dynamics. In the case of “aging”, i.e. pi being a decreasing function of its argument i, either the system reaches consensus or it gets trapped in a frozen state, depending on whether the limiting value p∞ is zero or positive, and on the rate at which pi approaches p∞. Moreover, when the system reaches consensus, the fraction x(t) of nodes not holding the consensus state may decay exponentially with time or as a power-law, depending again on the specific details of the functional form of pi. For the case of “anti-aging”, when the activation probability pi is an increasing function of i, the system always reaches a steady state with coexistence of opinions. Exact conditions for having one or another behavior, together with the equations and explicit expressions for the power-law exponents, are provided.

Suggested Citation

  • Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    • Handle: RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119314219
    DOI: 10.1016/j.physa.2019.122475
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    References listed on IDEAS

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    1. Vilela, André L.M. & Wang, Chao & Nelson, Kenric P. & Stanley, H. Eugene, 2019. "Majority-vote model for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 762-770.
    2. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2015. "Markets, herding and response to external information," Papers 1506.03708, arXiv.org, revised Jun 2015.
    3. Daniel M. Abrams & Steven H. Strogatz, 2003. "Modelling the dynamics of language death," Nature, Nature, vol. 424(6951), pages 900-900, August.
    4. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2016. "The noisy voter model on complex networks," Papers 1602.06935, arXiv.org, revised Apr 2016.
    5. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    6. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    7. Stauffer, Dietrich & Castelló, Xavier & Eguíluz, Víctor M. & San Miguel, Maxi, 2007. "Microscopic Abrams–Strogatz model of language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 835-842.
    8. Aleksejus Kononovicius & Julius Ruseckas, 2018. "Order book model with herd behavior exhibiting long-range memory," Papers 1809.02772, arXiv.org, revised Apr 2019.
    9. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    10. Jędrzejewski, Arkadiusz & Sznajd-Weron, Katarzyna, 2018. "Impact of memory on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 306-315.
    11. Adrián Carro & Raúl Toral & Maxi San Miguel, 2015. "Markets, Herding and Response to External Information," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-28, July.
    12. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    13. Alfarano, Simone & Milakovic, Mishael, 2009. "Network structure and N-dependence in agent-based herding models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 78-92, January.
    14. Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
    15. Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    16. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.
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    1. Khalil, Nagi, 2021. "Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Oestereich, André L. & Crokidakis, Nuno & Cajueiro, Daniel O., 2022. "Impact of memory and bias in kinetic exchange opinion models on random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.

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