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In a Nature article, Scheffer et al. presented a novel data-driven frameworkto predict critical transitions in complex systems. These transitions, whichmay stem from failures, degradation, or adversarial actions, have beenattributed to bifurcations in the nonlinear dynamics. Their approach was builtupon the phenomenon of critical slowing down, i.e., slow recovery in responseto small perturbations near bifurcations. We extend their approach to detectand localize critical transitions in nonlinear networks. By introducing thenotion of network critical slowing down, the objective of this paper is todetect that the network is undergoing a bifurcation only by analyzing itssignatures from measurement data. We focus on two classes of widely-usednonlinear networks: (1) Kuramoto model for the synchronization of coupledoscillators and (2) attraction-repulsion dynamics in swarms, each of whichpresents a specific type of bifurcation. Based on the phenomenon of criticalslowing down, we study the asymptotic behavior of the perturbed system away andclose to the bifurcation and leverage this fact to develop a deterministicmethod to detect and identify critical transitions in nonlinear networks.Furthermore, we study the state covariance matrix subject to a stochastic noiseprocess away and close to the bifurcation and use it to develop a stochasticframework for detecting critical transitions. Our simulation results show thestrengths and limitations of the methods.

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