| Piecewise linear differential equations and integrate-and-fire neurons: insights from two-dimensional membrane models. | |
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MedLine Citation:
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PMID: 12636716 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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We derive and study two-dimensional generalizations of integrate-and-fire models which can be found from a piecewise linear idealization of the FitzHugh-Nagumo or Morris-Lecar model. These models give rise to new properties not present in one-dimensional integrate-and-fire models. A detailed analytical study of the models is presented. In particular, (i) for the piecewise linear FitzHugh-Nagumo model, we determine analytically the bistability regime between stationary solutions and oscillations, that is, typical for class-II models. (ii) In the piecewise Morris-Lecar model, we find a noncanonical class-I transition from a stationary state to oscillations with logarithmic dependence similar to that found for leaky integrate-and-fire models. (iii) Furthermore, we establish a relation to the recently proposed resonate-and-fire model and show that a short input current pulse can trigger several spikes. |
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Authors:
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Arnaud Tonnelier; Wulfram Gerstner |
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Publication Detail:
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Type: Journal Article Date: 2003-02-19 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 67 ISSN: 1539-3755 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2003 Feb |
Date Detail:
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Created Date: 2003-03-14 Completed Date: 2003-06-30 Revised Date: 2003-11-04 |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 021908 Citation Subset: - |
Affiliation:
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Laboratory of Computational Neuroscience, EPFL, Lausanne, Switzerland. Arnaud.Tonnelier@epfl.ch |
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