Analysing and forecasting transitions in complex systems
File(s)
Author(s)
Piovani, Duccio
Type
Thesis
Abstract
We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element, the Stochastic Replicator model. A high dimensional stability matrix is derived for the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation we are able to construct a good early-warning indicator of the transitions occurring intermittently.
Version
Open Access
Date Issued
2015-09
Date Awarded
2016-03
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Jensen, Henrik
Grant Number
CONGAS (Grant FP7-ICT-2011-8-317672)
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)