Network Critical Slowing Down: Data-Driven Detection of Critical Transitions in Nonlinear Networks

TL;DR

This paper extends the concept of critical slowing down to nonlinear networks, proposing data-driven methods to detect and localize critical transitions such as bifurcations in systems like coupled oscillators and swarm dynamics.

Contribution

It introduces the notion of network critical slowing down and develops deterministic and stochastic methods for detecting bifurcations in nonlinear networks using measurement data.

Findings

Deterministic method effectively detects bifurcations in nonlinear networks.

Stochastic analysis using covariance matrices enhances detection near critical points.

Simulation results demonstrate the methods' strengths and limitations.

Abstract

In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to bifurcations in the nonlinear dynamics. Their approach was built upon the phenomenon of critical slowing down, i.e., slow recovery in response to small perturbations near bifurcations. We extend their approach to detect and localize critical transitions in nonlinear networks. By introducing the notion of network critical slowing down, the objective of this paper is to detect that the network is undergoing a bifurcation only by analyzing its signatures from measurement data. We focus on two classes of widely-used nonlinear networks: (1) Kuramoto model for the synchronization of coupled oscillators and (2) attraction-repulsion dynamics in swarms, each of which presents a specific type of bifurcation. Based on the phenomenon of critical slowing down, we study the asymptotic behavior of the perturbed system away and close to the bifurcation and leverage this fact to develop a deterministic method to detect and identify critical transitions in nonlinear networks. Furthermore, we study the state covariance matrix subject to a stochastic noise process away and close to the bifurcation and use it to develop a stochastic framework for detecting critical transitions. Our simulation results show the strengths and limitations of the methods.