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Firing map of an almost periodic input function

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  • In mathematical biology and the theory of electric networks the fi ring map of an integrate-and-fi re 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 simplifi ed model $ẋ$ = $f(t)$ still hold if $f \in L(^1_(loc))(R)$ 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).
    Mathematics Subject Classification: Primary: 37N25 42A75; Secondary: 37E45 92C20.


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