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Aging and equilibration in bistable contagion dynamics.

Paul Richter1, Malte Henkel2,3,4, Lucas Böttcher1,5,6

  • 1Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland.

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Summary
This summary is machine-generated.

This study reveals how contagion dynamics exhibit aging when initial states fall between stable attractors. This loss of time-translation invariance is key to understanding relaxation in complex systems.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Network science

Background:

  • Contagion models describe how states spread through networks.
  • Understanding relaxation dynamics and aging is crucial in many physical and social systems.
  • Time-translation invariance breaking is a hallmark of physical aging.

Purpose of the Study:

  • To analyze late-time relaxation dynamics in a general contagion model.
  • To investigate the conditions under which time-translation invariance is lost.
  • To characterize the model's behavior using a phase diagram.

Main Methods:

  • Analysis of late-time relaxation dynamics.
  • Identification of spontaneous and external failure mechanisms.
  • Mean-field predictions and phase diagram construction.
  • Examination of spatial correlation effects on square lattices.

Main Results:

  • Time-translation invariance is lost when initial conditions are between the two stable stationary states.
  • A phase diagram is established based on spontaneous and external failure fractions.
  • Spatial correlations on square lattices prevent linear separability of phases.
  • The model exhibits physical aging phenomena.

Conclusions:

  • The study provides insights into aging and relaxation in social contagion models.
  • The findings highlight the importance of initial conditions and network structure.
  • The developed phase diagram offers a framework for understanding system behavior.