Forecasting systemic transitions in high dimensional stochastic complex systems

摘要

We briefly describe a new procedure to monitor and forecast transitions occurring in high dimensional complex systems. The method is illustrated by applications to two model systems: firstly to the Tangled Nature Model of evolutionary ecology and secondly to a stochastic replicator system. The quasi-stable configurations of the stochastic dynamics are taken as input for a stability analysis of the deterministic mean field approximation of the dynamics. We demonstrate that the largest overlap between the observed configuration and the unstable eigendirections serves as a precursor that allows us to forecast transitions with an efficiency of about 80% even if we only know the couplings matrix describing the dynamics to with 10% accuracy.