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Predicting collapse of adaptive networked systems without knowing the network
The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6985233/ https://www.ncbi.nlm.nih.gov/pubmed/31988357 http://dx.doi.org/10.1038/s41598-020-57751-y |
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author | Horstmeyer, Leonhard Pham, Tuan Minh Korbel, Jan Thurner, Stefan |
author_facet | Horstmeyer, Leonhard Pham, Tuan Minh Korbel, Jan Thurner, Stefan |
author_sort | Horstmeyer, Leonhard |
collection | PubMed |
description | The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive change of network topology, usually accompanied by the extinction of a macroscopic fraction of nodes and links. It is often related to the breakdown of the last relevant directed catalytic cycle within a dynamical system. Without detailed structural information it seems impossible to state, whether a network is robust or if it is likely to collapse in the near future. Here we show that it is nevertheless possible to predict collapse for a large class of systems that are governed by a linear (or linearized) dynamics. To compute the corresponding early warning signal, we require only non-structural information about the nodes’ states such as species abundances in ecosystems, or company revenues in economic networks. It is shown that the existence of a single directed cycle in the network can be detected by a “quantization effect” of node states, that exists as a direct consequence of a corollary of the Perron–Frobenius theorem. The proposed early warning signal for the collapse of networked systems captures their structural instability without relying on structural information. We illustrate the validity of the approach in a transparent model of co-evolutionary ecosystems and show this quantization in systems of species evolution, epidemiology, and population dynamics. |
format | Online Article Text |
id | pubmed-6985233 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-69852332020-01-31 Predicting collapse of adaptive networked systems without knowing the network Horstmeyer, Leonhard Pham, Tuan Minh Korbel, Jan Thurner, Stefan Sci Rep Article The collapse of ecosystems, the extinction of species, and the breakdown of economic and financial networks usually hinges on topological properties of the underlying networks, such as the existence of self-sustaining (or autocatalytic) feedback cycles. Such collapses can be understood as a massive change of network topology, usually accompanied by the extinction of a macroscopic fraction of nodes and links. It is often related to the breakdown of the last relevant directed catalytic cycle within a dynamical system. Without detailed structural information it seems impossible to state, whether a network is robust or if it is likely to collapse in the near future. Here we show that it is nevertheless possible to predict collapse for a large class of systems that are governed by a linear (or linearized) dynamics. To compute the corresponding early warning signal, we require only non-structural information about the nodes’ states such as species abundances in ecosystems, or company revenues in economic networks. It is shown that the existence of a single directed cycle in the network can be detected by a “quantization effect” of node states, that exists as a direct consequence of a corollary of the Perron–Frobenius theorem. The proposed early warning signal for the collapse of networked systems captures their structural instability without relying on structural information. We illustrate the validity of the approach in a transparent model of co-evolutionary ecosystems and show this quantization in systems of species evolution, epidemiology, and population dynamics. Nature Publishing Group UK 2020-01-27 /pmc/articles/PMC6985233/ /pubmed/31988357 http://dx.doi.org/10.1038/s41598-020-57751-y Text en © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Horstmeyer, Leonhard Pham, Tuan Minh Korbel, Jan Thurner, Stefan Predicting collapse of adaptive networked systems without knowing the network |
title | Predicting collapse of adaptive networked systems without knowing the network |
title_full | Predicting collapse of adaptive networked systems without knowing the network |
title_fullStr | Predicting collapse of adaptive networked systems without knowing the network |
title_full_unstemmed | Predicting collapse of adaptive networked systems without knowing the network |
title_short | Predicting collapse of adaptive networked systems without knowing the network |
title_sort | predicting collapse of adaptive networked systems without knowing the network |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6985233/ https://www.ncbi.nlm.nih.gov/pubmed/31988357 http://dx.doi.org/10.1038/s41598-020-57751-y |
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