Forecasting systemic transitions in high dimensional stochastic complex systems

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Piovani, Duccio^1 ; Grujic, Jelena^1 ; Jensen, Henrik Jeldtoft^1

Centre for Complexity Science, Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, United Kingdom^1

关键词: A-stability;    Evolutionary ecology;    Forecast transitions;    High-dimensional;    Mean field approximation;    Stable Configuration;    Stochastic dynamics;    Two model systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012001/pdf
DOI  :  10.1088/1742-6596/633/1/012001

来源: IOP

【 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.