Aging and equilibration in bistable contagion dynamics

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.