TY - JOUR

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

AU - Ivanov, Anatoli F.

AU - Trofimchuk, Sergei I.

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

VL - 252

SP - 446

EP - 456

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -