Phase-amplitude descriptions of neural oscillator models
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...
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Springer
2013
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| Online Access: | https://eprints.nottingham.ac.uk/1896/ |
| _version_ | 1848790681462505472 |
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| author | Wedgwood, Kyle C.A. Lin, Kevin K. Thul, Ruediger Coombes, Stephen |
| author_facet | Wedgwood, Kyle C.A. Lin, Kevin K. Thul, Ruediger Coombes, Stephen |
| author_sort | Wedgwood, Kyle C.A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:16:29Z |
| format | Article |
| id | nottingham-1896 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:16:29Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-18962020-05-04T20:20:56Z https://eprints.nottingham.ac.uk/1896/ Phase-amplitude descriptions of neural oscillator models Wedgwood, Kyle C.A. Lin, Kevin K. Thul, Ruediger Coombes, Stephen 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. Springer 2013 Article PeerReviewed Wedgwood, Kyle C.A., Lin, Kevin K., Thul, Ruediger and Coombes, Stephen (2013) Phase-amplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3 (2). ISSN 2190-8567 http://www.mathematical-neuroscience.com/content/3/1/2 doi:10.1186/2190-8567-3-2 doi:10.1186/2190-8567-3-2 |
| spellingShingle | Wedgwood, Kyle C.A. Lin, Kevin K. Thul, Ruediger Coombes, Stephen Phase-amplitude descriptions of neural oscillator models |
| title | Phase-amplitude descriptions of neural oscillator models |
| title_full | Phase-amplitude descriptions of neural oscillator models |
| title_fullStr | Phase-amplitude descriptions of neural oscillator models |
| title_full_unstemmed | Phase-amplitude descriptions of neural oscillator models |
| title_short | Phase-amplitude descriptions of neural oscillator models |
| title_sort | phase-amplitude descriptions of neural oscillator models |
| url | https://eprints.nottingham.ac.uk/1896/ https://eprints.nottingham.ac.uk/1896/ https://eprints.nottingham.ac.uk/1896/ |