Sharpening the Universality of Network Resilience Patterns using Motifs

Abstract

The resilience of networked systems to perturbations is a fundamental problem with applications to ecosystem management, financial system stability, and cell reprogramming. This key challenge is that in high-dimensional systems, there is no “oracle” that can predict, a priori, which changes to a nonlinear system’s parameters will be harmless vs. which will cause a system-wide failure (bifurcation). Here, we present a proof of principle using the Florida Bay food web network, showing how one can use higher-order network structure to arrive at a reliable, universal scalar indicator of a system’s proximity to a bifurcation. Our framework builds on and sharpens a recently introduced mean-field theory for nonlinear dynamics on networks. We find that by incorporating information on high-order network structure in the form of network motifs, the prediction of resilience is greatly improved, especially near a bifurcation point. Our results stress the key role of higher-order structure in driving a system’s dynamics, offering new ways to anticipate and prevent the collapse of large networks raging from ecosystems to infrastructure networks.