Firing map of an almost periodic input function

Wacław Marzantowicz; Justyna Signerska-Rynkowska

doi:10.3934/proc.2011.2011.1032

Firing map of an almost periodic input function

Abstract

In mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still hold if f∈L(1(loc))(R) and f is an almost periodic function. Moreover, in this way we prepare a formal framework for next study of a discrete dynamics of the firing map arising from almost periodic stimulus that gives information on consecutive resets (spikes).

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Authors (2)

Wacław Marzantowicz
- Adam Mickiewicz University of Poznań Faculty of Mathematics and Computer Sci.,
Justyna Signerska-Rynkowska dr inż.
- olish Academy of Sciences Institute of Mathematics

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DOI:: Digital Object Identifier (open in new tab) 10.3934/proc.2011.2011.1032
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Category:: Other
Type:: supllement, wydanie specjalne, dodatek
Published in:: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS no. Special Issue, pages 1032 - 1041,
ISSN: 1078-0947
Language:: English
Publication year:: 2011
DOI:: Digital Object Identifier (open in new tab) 10.3934/proc.2011.2011.1032
Verified by:: Gdańsk University of Technology