dc.contributor.author | Ashwin, Peter | |
dc.contributor.author | Coombes, S | |
dc.contributor.author | Nicks, R | |
dc.date.accessioned | 2016-02-09T15:34:34Z | |
dc.date.issued | 2016-01-06 | |
dc.description.abstract | 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 mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience. | en_GB |
dc.description.sponsorship | European Commission, FP7 Marie Curie Initial Training Network | en_GB |
dc.description.sponsorship | NETT: Neural Engineering Transformative Technologies | en_GB |
dc.identifier.citation | Vol. 6, pp. 2 - | en_GB |
dc.identifier.doi | 10.1186/s13408-015-0033-6 | |
dc.identifier.grantnumber | 289146 | en_GB |
dc.identifier.other | 10.1186/s13408-015-0033-6 | |
dc.identifier.uri | http://hdl.handle.net/10871/19672 | |
dc.language.iso | en | en_GB |
dc.publisher | BioMed Central | en_GB |
dc.relation.url | http://www.ncbi.nlm.nih.gov/pubmed/26739133 | en_GB |
dc.rights | Copyright © 2016 Ashwin et al. This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided 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. | en_GB |
dc.subject | Central pattern generator | en_GB |
dc.subject | Chimera state | en_GB |
dc.subject | Coupled oscillator network | en_GB |
dc.subject | Groupoid formalism | en_GB |
dc.subject | Heteroclinic cycle | en_GB |
dc.subject | Isochrons | en_GB |
dc.subject | Master stability function | en_GB |
dc.subject | Network motif | en_GB |
dc.subject | Perceptual rivalry | en_GB |
dc.subject | Phase oscillator | en_GB |
dc.subject | Phase–amplitude coordinates | en_GB |
dc.subject | Stochastic oscillator | en_GB |
dc.subject | Strongly coupled integrate-and-fire network | en_GB |
dc.subject | Symmetric dynamics | en_GB |
dc.subject | Weakly coupled phase oscillator network | en_GB |
dc.subject | Winfree model | en_GB |
dc.title | Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2016-02-09T15:34:34Z | |
dc.identifier.issn | 2190-8567 | |
exeter.place-of-publication | Germany | |
dc.description | Published | en_GB |
dc.description | Journal Article | en_GB |
dc.identifier.journal | Journal of Mathematical Neuroscience | en_GB |