Singularly perturbed phase response curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866909186546204672 |
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| author | Sacré, Pierre Franci, Alessio |
| author_facet | Sacré, Pierre Franci, Alessio |
| contents | In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the methodology by deriving semi-analytic formula for the (finite) phase response curve of generic planar relaxation oscillators to impulses and square pulses of finite duration and verify its goodness numerically on the FitzHugh-Nagumo model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_02010 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Singularly perturbed phase response curves Sacré, Pierre Franci, Alessio Dynamical Systems In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the infinitesimal phase response curve approach to relaxation oscillators and overcomes its limitations near the singular limit. We illustrate the power of the methodology by deriving semi-analytic formula for the (finite) phase response curve of generic planar relaxation oscillators to impulses and square pulses of finite duration and verify its goodness numerically on the FitzHugh-Nagumo model. |
| title | Singularly perturbed phase response curves |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/1506.02010 |