Phase-Amplitude Descriptions of Neural Oscillator Models

Persistent Link:
http://hdl.handle.net/10150/610255
Title:
Phase-Amplitude Descriptions of Neural Oscillator Models
Author:
Wedgwood, Kyle C. A.; Lin, Kevin K.; Thul, Ruediger; Coombes, Stephen
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK; Department of Applied Mathematics, University of Arizona, Tucson, AZ, USA
Issue Date:
2013
Publisher:
BioMed Central
Citation:
Journal of Mathematical Neuroscience (2013) 3:2 DOI 10.1186/2190-8567-3-2
Journal:
The Journal of Mathematical Neuroscience
Rights:
© 2013 K.C.A. Wedgwood et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0)
Collection Information:
This item is part of the UA Faculty Publications collection. For more information this item or other items in the UA Campus Repository, contact the University of Arizona Libraries at repository@u.library.arizona.edu.
Abstract:
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.
EISSN:
2190-8567
DOI:
10.1186/2190-8567-3-2
Keywords:
Phase-amplitude; Oscillator; Chaos; Non-weak coupling
Version:
Final published version
Additional Links:
http://www.mathematical-neuroscience.com/content/3/1/2

Full metadata record

DC FieldValue Language
dc.contributor.authorWedgwood, Kyle C. A.en
dc.contributor.authorLin, Kevin K.en
dc.contributor.authorThul, Ruedigeren
dc.contributor.authorCoombes, Stephenen
dc.date.accessioned2016-05-20T09:02:19Z-
dc.date.available2016-05-20T09:02:19Z-
dc.date.issued2013en
dc.identifier.citationJournal of Mathematical Neuroscience (2013) 3:2 DOI 10.1186/2190-8567-3-2en
dc.identifier.doi10.1186/2190-8567-3-2en
dc.identifier.urihttp://hdl.handle.net/10150/610255-
dc.description.abstractPhase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.en
dc.language.isoenen
dc.publisherBioMed Centralen
dc.relation.urlhttp://www.mathematical-neuroscience.com/content/3/1/2en
dc.rights© 2013 K.C.A. Wedgwood et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0)en
dc.subjectPhase-amplitudeen
dc.subjectOscillatoren
dc.subjectChaosen
dc.subjectNon-weak couplingen
dc.titlePhase-Amplitude Descriptions of Neural Oscillator Modelsen
dc.typeArticleen
dc.identifier.eissn2190-8567en
dc.contributor.departmentSchool of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UKen
dc.contributor.departmentDepartment of Applied Mathematics, University of Arizona, Tucson, AZ, USAen
dc.identifier.journalThe Journal of Mathematical Neuroscienceen
dc.description.collectioninformationThis item is part of the UA Faculty Publications collection. For more information this item or other items in the UA Campus Repository, contact the University of Arizona Libraries at repository@u.library.arizona.edu.en
dc.eprint.versionFinal published versionen
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