Forecasting transitions in systems with high dimensional stochastic complex dynamics: A Linear Stability Analysis of the Tangled Nature Model

TL;DR

This paper introduces a method to forecast transitions in high-dimensional stochastic systems by combining stability analysis of mean field equations with stochastic configuration monitoring, demonstrated on an ecological model.

Contribution

It presents a novel approach that uses eigenvalue analysis of mean field stability matrices to predict transitions in complex stochastic systems.

Findings

Eigenvalues with positive real parts indicate unstable directions.

Overlap with unstable eigenvectors serves as an early warning signal.

Method successfully predicts transitions in the Tangled Nature model.

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 quasi-stable 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 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.