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Linear stability theory as an early warning sign for transitions in high dimensional complex systems

Piovani, D; Grujic, J; Jensen, HJ; (2016) Linear stability theory as an early warning sign for transitions in high dimensional complex systems. Journal of Physics A: Mathematical and Theoretical , 49 (29) , Article 295102. 10.1088/1751-8113/49/29/295102. Green open access

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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. A high dimensional stability matrix is derived in 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.

Type: Article
Title: Linear stability theory as an early warning sign for transitions in high dimensional complex systems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1751-8113/49/29/295102
Publisher version: https://doi.org/10.1088/1751-8113/49/29/295102
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Mathematical, Physics, forecasting critical transitions, adaptive systems, evolutionary dynamics, replicator system, MODEL, EVOLUTION, EMERGENCE, SELECTION, DYNAMICS, MUTATION
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment
URI: https://discovery.ucl.ac.uk/id/eprint/10067849
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