| 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cooperative</i> (network layers mutually depend on one another) or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-cooperative</i> (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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimization of coupling asymmetry and timescale balancing</i> as fundamental concepts for the design of collective behavior over interconnected systems. |
, Dane Taylor 
