Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive

Justyna Signerska-Rynkowska

doi:10.3846/13926292.2015.1085459

Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive

Abstract

We study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle homeomorphism, we provide a detailed description of the regularity properties of the sequence of interspike-intervals and behaviour of the interspike-interval distribution.

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Justyna Signerska-Rynkowska dr inż.
- Polish Academy Science Institute of Mathematics

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DOI:: Digital Object Identifier (open in new tab) 10.3846/13926292.2015.1085459
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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: Mathematical Modelling and Analysis no. 20, edition 5, pages 529 - 551,
ISSN: 1392-6292
Language:: English
Publication year:: 2015
Bibliographic description:: Signerska-Rynkowska J.: Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive// Mathematical Modelling and Analysis. -Vol. 20, iss. 5 (2015), s.529-551
DOI:: Digital Object Identifier (open in new tab) 10.3846/13926292.2015.1085459
Verified by:: Gdańsk University of Technology