Coupling Asymmetry Optimizes Collective Dynamics over Multiplex Networks

TL;DR

This paper investigates how asymmetrical coupling in multiplex networks affects collective dynamics, revealing that optimal asymmetry can significantly accelerate convergence and depend on the relative timescales of interconnected systems.

Contribution

It introduces a generalized graph Laplacian framework to analyze the nonlinear effects of coupling asymmetry on collective phenomena in multiplex networks.

Findings

Asymmetry induces multiple optima for convergence acceleration.

Optimal coupling depends on the relative timescales of network layers.

A human-AI decision-making model demonstrates the importance of timescale similarity.

Abstract

Networks are often interconnected, with one system wielding greater influence over another. However, the effects of such asymmetry on self-organized phenomena (e.g., consensus and synchronization) are not well understood. Here, we study collective dynamics using a generalized graph Laplacian for multiplex networks containing layers that are asymmetrically coupled. We explore the nonlinear effects of coupling asymmetry on the convergence rate toward a collective state, finding that asymmetry induces one or more optima that maximally accelerate convergence. When a faster and a slower system are coupled, depending on their relative timescales, their optimal coupling is either cooperative (network layers mutually depend on one another) or non-cooperative (one network directs another without a reciprocated influence). It is often optimal for the faster system to more-strongly influence the slower one, yet counter-intuitively, the opposite can also be true. As an application, we model collective decision-making for a human-AI system in which a social network is supported by an AI-agent network, finding that a cooperative optimum requires that these two networks operate on a sufficiently similar timescale. More broadly, our work highlights the optimization of coupling asymmetry and timescale balancing as fundamental concepts for the design of collective behavior over interconnected systems.