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Heteroclinic networks for brain dynamics
Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the correspo...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Frontiers Media S.A.
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10663269/ https://www.ncbi.nlm.nih.gov/pubmed/38020242 http://dx.doi.org/10.3389/fnetp.2023.1276401 |
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author | Meyer-Ortmanns, Hildegard |
author_facet | Meyer-Ortmanns, Hildegard |
author_sort | Meyer-Ortmanns, Hildegard |
collection | PubMed |
description | Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka–Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research. |
format | Online Article Text |
id | pubmed-10663269 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Frontiers Media S.A. |
record_format | MEDLINE/PubMed |
spelling | pubmed-106632692023-11-08 Heteroclinic networks for brain dynamics Meyer-Ortmanns, Hildegard Front Netw Physiol Network Physiology Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka–Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research. Frontiers Media S.A. 2023-11-08 /pmc/articles/PMC10663269/ /pubmed/38020242 http://dx.doi.org/10.3389/fnetp.2023.1276401 Text en Copyright © 2023 Meyer-Ortmanns. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. |
spellingShingle | Network Physiology Meyer-Ortmanns, Hildegard Heteroclinic networks for brain dynamics |
title | Heteroclinic networks for brain dynamics |
title_full | Heteroclinic networks for brain dynamics |
title_fullStr | Heteroclinic networks for brain dynamics |
title_full_unstemmed | Heteroclinic networks for brain dynamics |
title_short | Heteroclinic networks for brain dynamics |
title_sort | heteroclinic networks for brain dynamics |
topic | Network Physiology |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10663269/ https://www.ncbi.nlm.nih.gov/pubmed/38020242 http://dx.doi.org/10.3389/fnetp.2023.1276401 |
work_keys_str_mv | AT meyerortmannshildegard heteroclinicnetworksforbraindynamics |