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Aging in binary-state models: The Threshold model for complex contagion.

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Aging in complex networks slows technology adoption dynamics. This study analyzes non-Markovian aging effects on the Threshold model, finding slower cascade dynamics but unchanged adoption conditions across various network types.

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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • The Threshold model explains technology adoption but often assumes homogeneous agent behavior.
  • Aging, where agents resist state changes over time, introduces heterogeneity and non-Markovian dynamics.
  • Understanding these dynamics is crucial for modeling real-world adoption processes.

Purpose of the Study:

  • To investigate the impact of non-Markovian aging on binary-state dynamics within the Threshold model.
  • To analyze how aging affects cascade conditions and adoption speed in different network structures.
  • To develop analytical approximations for aging effects and compare them with simulation results.

Main Methods:

  • Analytical approximations were developed to describe aging effects.
  • Extensive Monte Carlo simulations were performed on Erdős-Rényi, random-regular, and Barabási-Albert networks.
  • Simulations were also conducted on a two-dimensional lattice to assess aging in different network topologies.

Main Results:

  • Aging does not alter the fundamental condition for adoption cascades.
  • Aging significantly slows down the speed of cascade dynamics towards full adoption.
  • The adoption growth law changes from exponential to stretched exponential or power law, depending on the aging mechanism.
  • Analytical expressions for cascade conditions and growth law exponents were derived.

Conclusions:

  • Non-Markovian aging introduces significant temporal heterogeneity in agent behavior.
  • While not preventing adoption cascades, aging modifies their temporal evolution, leading to slower adoption rates.
  • The findings provide a more realistic framework for modeling technology adoption and other social contagion processes in complex systems.