Equation-Free Multiscale Computations in Social Networks: from Agent-based Modelling to Coarse-grained Stability and Bifurcation Analysis

TL;DR

This paper demonstrates how the Equation-Free multiscale computational framework can analyze emergent social network dynamics, revealing stable states and bifurcations from agent-based models to system-level insights.

Contribution

It introduces a novel application of the Equation-Free approach to social networks, enabling coarse-grained stability and bifurcation analysis from agent-based models.

Findings

Multiple stable states depend on network topology

Bifurcation diagrams reveal stability changes in social dynamics

Equation-Free method bridges agent models with continuum analysis

Abstract

We focus at the interface between multiscale computations, bifurcation theory and social networks. In particular we address how the Equation-Free approach, a recently developed computational framework, can be exploited to systematically extract coarse-grained, emergent dynamical information by bridging detailed, agent-based models of social interactions on networks, with macroscopic, systems-level, continuum numerical analysis tools. For our illustrations we use a simple dynamic agent-based model describing the propagation of information between individuals interacting under mimesis in a social network with private and public information. We describe the rules governing the evolution of the agents emotional state dynamics and discover, through simulation, multiple stable stationary states as a function of the network topology. Using the Equation-Free approach we track the dependence of these stationary solutions on network parameters and quantify their stability in the form of coarse-grained bifurcation diagrams.