TY - JOUR

T1 - On global dynamics in a periodic differential equation with deviating argument

AU - Ivanov, Anatoli F.

AU - Trofimchuk, Sergei I.

N1 - Funding Information:
This research was partially supported through the programme ”Research in Pairs” by the Mathematisches Forschungsinstitut Oberwolfach in 2013 (A. Ivanov). Additionally, A. Ivanov and S. Trofimchuk were supported by the CONICYT grant 80110006 and the IMAP (University of Talca, Chile). We would like to thank Penn State students Artem Morozov and Dashiel Lopez Mendez for their computational and graphical work some of which is used in this paper. They have done this work within a PSU W-B undergraduate student research project. We are thankful to the anonymous referees for their critical remarks and suggestions, which have helped us to substantially improve this paper.
Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - 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 · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x 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).

AB - 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 · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x 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).

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U2 - 10.1016/j.amc.2014.12.015

DO - 10.1016/j.amc.2014.12.015

M3 - Article

AN - SCOPUS:84920193218

SN - 0096-3003

VL - 252

SP - 446

EP - 456

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -