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Non-Markovian majority-vote model.

Hanshuang Chen1, Shuang Wang1, Chuansheng Shen2

  • 1School of Physics and Materials Science, Anhui University, Hefei 230601, China.

Physical Review. E
|January 20, 2021
PubMed
Summary

We introduce a non-Markovian majority-vote model (NMMV) incorporating agent age into opinion dynamics. This aging or anti-aging process non-monotonically affects the critical noise, showing optimal rates for transition perturbation.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Social dynamics

Background:

  • Non-Markovian dynamics, characterized by memory effects and burstiness, are prevalent in human activities and social networks.
  • Standard majority-vote models (SMV) are simple Markovian models for opinion dynamics, exhibiting a continuous phase transition.
  • Understanding memory effects in opinion dynamics is crucial for modeling real-world social behaviors.

Purpose of the Study:

  • To propose and analyze a non-Markovian majority-vote model (NMMV) that incorporates agent 'age' (time in current state).
  • To investigate how aging and anti-aging dynamics influence opinion formation and phase transitions.
  • To determine the impact of aging/anti-aging rates on the critical noise of the opinion dynamics.

Main Methods:

  • Development of the non-Markovian majority-vote model (NMMV) with age-dependent state change probabilities.
  • Analysis using the heterogeneous mean-field approach for analytical insights.
  • Validation through extensive numerical simulations across diverse network topologies.

Main Results:

  • The critical noise for the order-disorder phase transition becomes a non-monotonic function of the aging/anti-aging rate (β).
  • In the aging regime, critical noise shows a maximum with respect to β; in the anti-aging regime, it shows a minimum.
  • Optimal aging/anti-aging rates exist that maximally perturb the critical noise value.

Conclusions:

  • Agent age significantly alters opinion dynamics, introducing non-Markovian memory effects.
  • Aging and anti-aging processes can effectively retard or anticipate the opinion transition.
  • The NMMV provides a more realistic framework for understanding opinion dynamics in social systems with memory effects.