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On the interspike-intervals of periodically-driven integrate-and-fire models

Abstract

We analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical study of the displacement sequence of an orientation preserving circle homeomorphism, we provide a complete description of regularity properties of the sequence of interspike-intervals and behaviour of the interspike-interval distribution. Our results allow to explain some facts concerning this distribution observed numerically by other authors. These theoretical findings are illustrated by computational examples.

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Authors (2)

  • Photo of  Wacław Marzantowicz

    Wacław Marzantowicz

    • Adam Mickiewicz University of Poznań Faculty of Mathematics and Computer Sci
  • Photo of dr inż. Justyna Signerska-Rynkowska

    Justyna Signerska-Rynkowska dr inż.

    • Polish Academy of Sciences Institute of Mathematics

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Accepted or Published Version
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2014.10.013
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Copyright (2014 Elsevier Inc)

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Details

Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS no. 423, edition 1, pages 456 - 479,
ISSN: 0022-247X
Language:
English
Publication year:
2015
Bibliographic description:
Marzantowicz W., Signerska-Rynkowska J.: On the interspike-intervals of periodically-driven integrate-and-fire models// JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. -Vol. 423, iss. 1 (2015), s.456-479
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2014.10.013
Verified by:
Gdańsk University of Technology

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