Mathematical frameworks for oscillatory network dynamics in neuroscience
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there...
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| Format: | Article |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/41034/ |
| _version_ | 1848796181746941952 |
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| author | Ashwin, Peter Coombes, Stephen Nicks, Rachel |
| author_facet | Ashwin, Peter Coombes, Stephen Nicks, Rachel |
| author_sort | Ashwin, Peter |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience. |
| first_indexed | 2025-11-14T19:43:54Z |
| format | Article |
| id | nottingham-41034 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:54Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410342020-05-04T17:33:14Z https://eprints.nottingham.ac.uk/41034/ Mathematical frameworks for oscillatory network dynamics in neuroscience Ashwin, Peter Coombes, Stephen Nicks, Rachel The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience. Springer 2016-01-06 Article PeerReviewed Ashwin, Peter, Coombes, Stephen and Nicks, Rachel (2016) Mathematical frameworks for oscillatory network dynamics in neuroscience. Journal of Mathematical Neuroscience, 6 . 2/1-2/92. ISSN 2190-8567 Central pattern generator Chimera state Coupled oscillator network Groupoid formalism Heteroclinic cycle Isochrons Master stability function Network motif Perceptual rivalry Phase oscillator Phase–amplitude coordinates Stochastic oscillator Strongly coupled integrate-and-fire network Symmetric dynamics Weakly coupled phase oscillator network Winfree model http://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-015-0033-6 doi:10.1186/s13408-015-0033-6 doi:10.1186/s13408-015-0033-6 |
| spellingShingle | Central pattern generator Chimera state Coupled oscillator network Groupoid formalism Heteroclinic cycle Isochrons Master stability function Network motif Perceptual rivalry Phase oscillator Phase–amplitude coordinates Stochastic oscillator Strongly coupled integrate-and-fire network Symmetric dynamics Weakly coupled phase oscillator network Winfree model Ashwin, Peter Coombes, Stephen Nicks, Rachel Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title | Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title_full | Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title_fullStr | Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title_full_unstemmed | Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title_short | Mathematical frameworks for oscillatory network dynamics in neuroscience |
| title_sort | mathematical frameworks for oscillatory network dynamics in neuroscience |
| topic | Central pattern generator Chimera state Coupled oscillator network Groupoid formalism Heteroclinic cycle Isochrons Master stability function Network motif Perceptual rivalry Phase oscillator Phase–amplitude coordinates Stochastic oscillator Strongly coupled integrate-and-fire network Symmetric dynamics Weakly coupled phase oscillator network Winfree model |
| url | https://eprints.nottingham.ac.uk/41034/ https://eprints.nottingham.ac.uk/41034/ https://eprints.nottingham.ac.uk/41034/ |