Early-warning signals using dynamical network markers selected by covariance

It is an important issue, particularly in the context of sustainable society, to predict critical transitions across which a system state abruptly shifts toward a contrasting state. In this study, we propose an indicator of critical transitions in multivariate dynamical systems, based on the concept of the dynamical network marker (DNM). The DNM is originally defined based on the eigendecomposition of the Jacobian matrix of a nonlinear system and corresponds to large-magnitude components of the dominant eigenvector, which contributes primarily to transitions. Our DNM-based indicator is derived from the sample covariance matrix of state variables in a target system. Simulation results to predict transitions in complex network systems consisting of a harvesting model consistently show the superiority of our indicator as a precursor of transitions regardless of network structure characteristics, as compared to a conventional indicator.