Sustained oscillations in multi-topic belief dynamics over signed networks

TL;DR

This paper investigates how beliefs about multiple topics evolve over interconnected networks, identifying conditions that lead to persistent oscillations in beliefs due to network structure and dynamics.

Contribution

It provides a theoretical analysis of sustained belief oscillations in multi-topic networks, linking network topology to oscillation patterns and bifurcation conditions.

Findings

Sustained oscillations occur via Hopf bifurcation under specific conditions.

Network structure critically influences oscillation patterns.

Certain classes of graphs do not exhibit oscillations.

Abstract

We study the dynamics of belief formation on multiple interconnected topics in networks of agents with a shared belief system. We establish sufficient conditions and necessary conditions under which sustained oscillations of beliefs arise on the network in a Hopf bifurcation and characterize the role of the communication graph and the belief system graph in shaping the relative phase and amplitude patterns of the oscillations. Additionally, we distinguish broad classes of graphs that exhibit such oscillations from those that do not.