Aging and equilibration in bistable contagion dynamics

TL;DR

This paper investigates the late-time relaxation and aging phenomena in a bistable contagion model, revealing how initial conditions influence long-term dynamics and phase behavior in social contagion processes.

Contribution

It introduces a comprehensive analysis of aging in a bistable contagion model, highlighting the effects of spatial correlations and initial conditions on relaxation dynamics.

Findings

Time-translation invariance is broken for certain initial conditions.

Phase diagram characterizes the fractions of failed nodes and their effects.

Spatial correlations prevent linear separability of phases on a square lattice.

Abstract

We analyze the late-time relaxation dynamics for a general contagion model. In this model, nodes are either active or failed. Active nodes can fail either "spontaneously" at any time or "externally" if their neighborhoods are sufficiently damaged. Failed nodes may always recover spontaneously. At late times, the breaking of time-translation-invariance is a necessary condition for physical aging. We observe that time-translational invariance is lost for initial conditions that lie between the basins of attraction of the model's two stable stationary states. Based on corresponding mean-field predictions, we characterize the observed model behavior in terms of a phase diagram spanned by the fractions of spontaneously and externally failed nodes. For the square lattice, the phases in which the dynamics approaches one of the two stable stationary states are not linearly separable due to spatial correlation effects. Our results provide new insights into aging and relaxation phenomena that are observable in a model of social contagion processes.