Memory-induced mechanism for self-sustaining activity in networks

TL;DR

This paper investigates a novel memory-based mechanism for self-sustaining activity in networks, emphasizing tree-like structures and temporal memory, with implications for social media dynamics and attention redistribution.

Contribution

It introduces a new model of activity sustainment based on temporal memory in tree-like networks, contrasting with loop-dependent models, and explores the effects of behavioral noise and connection strength changes.

Findings

Nodes form clusters with partial synchronization under weak noise.

Memory mechanisms enable activity sustainment without network loops.

Changing connection strengths facilitates self-sustained activity.

Abstract

We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the activity provided initially is sustained within the collective of interacting agents. In contrast to existing models of self-sustaining activity that are caused by (long) loops present in the network, here we focus on tree--like structures and examine activation mechanisms that are due to temporal memory of the nodes. This approach is motivated by applications in social media, where long network loops are rare or absent. Our results suggest that under a weak behavioral noise, the nodes robustly split into several clusters, with partial synchronization of nodes within each cluster. We also study the randomly-weighted version of the models where the nodes are allowed to change their connection strength (this can model attention redistribution), and show that it does facilitate the self-sustained activity.