## On periodic solutions and global dynamics in a periodic differential delay equation

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##### Date

2014-05-13##### MFO Scientific Program

Research in Pairs 2013##### Series

Oberwolfach Preprints;2014,08##### Author

Ivanov, Anatoli F.

Trofimchuk, Sergei I.

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Show full item record##### OWP-2014-08

##### Abstract

Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation $x'(t) = a(t)f(x([t-K]))$, where $f(x)$ is a continuous negative feedback function, $x \cdot f(x) < 0 x \neq 0, 0\leq a(t)$ is continuous $\omega$-periodic, $[\cdot]$ is the integer part function, and the integer $K \geq 0$ is the delay. The case of integer period $\omega$ allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps $(K = 0)$.