On global dynamics in a periodic differential equation with deviating argument

Anatoli Ivanov, Sergei I. Trofimchuk

Research output: Contribution to journalArticle

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 · 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).

Original language English (US) 446-456 11 Applied Mathematics and Computation 252 https://doi.org/10.1016/j.amc.2014.12.015 Published - Feb 1 2015

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Deviating Argument
Global Dynamics
Differential equations
Differential equation
Integer
Difference equations
Differential Delay Equations
Interval Maps
Negative Feedback
Feedback
Difference equation
Periodic Solution
Scalar
Partial

All Science Journal Classification (ASJC) codes

• Computational Mathematics
• Applied Mathematics

Cite this

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On global dynamics in a periodic differential equation with deviating argument. / Ivanov, Anatoli; Trofimchuk, Sergei I.

In: Applied Mathematics and Computation, Vol. 252, 01.02.2015, p. 446-456.

Research output: Contribution to journalArticle

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