Early Warnings for Multistage Transitions in Dynamics on Networks

TL;DR

This paper develops methods to predict multistage transitions in networked systems by identifying key nodes that serve as early warning signals, improving anticipation of regime shifts.

Contribution

It introduces a framework for calculating early warning signals in multistage network transitions and identifies optimal sentinel nodes depending on transition stages and directions.

Findings

Small subsets of nodes can effectively predict transitions.

Knowledge of network structure improves warning signals.

No universal sentinel nodes; optimal nodes vary with transition stage.

Abstract

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked systems undergoing a multistage transition. We found that knowledge of both the ongoing multistage transition and network structure enables us to calculate effective early warning signals for multistage transitions. Furthermore, we found that small subsets of nodes could anticipate transitions as well as or even better than using all the nodes. Even if we fix the network and dynamical system, no single best subset of nodes provides good early warning signals, and a good choice of sentinel nodes depends on the tipping direction and the current stage of the dynamics within a multistage transition, which we systematically characterize.