Interaction Network, State Space and Control in Social Dynamics

TL;DR

This paper investigates how interaction networks and state spaces influence the emergence of global patterns in large multi-agent systems, exploring conditions for convergence and control strategies for systems that do not naturally reach desired equilibria.

Contribution

It introduces a comprehensive analysis of the roles of interaction networks and state spaces in social dynamics and proposes control methods for non-converging systems.

Findings

Connectivity influences convergence to equilibria

State space determines possible equilibrium types

Control can steer systems towards desired states

Abstract

In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state space determines the types of equilibrium that can be reached by the system. Meanwhile, convergence to specific equilibria depends on the connectivity of the interaction network and on the interaction potential. When the system does not satisfy the necessary conditions for convergence to the desired equilibrium, control can be exerted, both on finite-dimensional systems and on their mean-field limit.