Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model

Phys Rev Lett. 2014 Dec 31;113(26):264102. doi: 10.1103/PhysRevLett.113.264102. Epub 2014 Dec 24.

Abstract

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.