TY - JOUR

T1 - Periodic solutions of a discretized differential delay equation

AU - Ivanov, Anatoli F.

AU - Trofimchuk, Sergei I.

N1 - Funding Information:
This research was supported in part by the NSF grant INT-0203702 (Anatoli F. Ivanov) and by the FONDECYT project 1071053 and University of Talca Program ‘Reticulados y Ecuaciones’ (Sergei I. Trofimchuk).

PY - 2010/2

Y1 - 2010/2

N2 - Several aspects of dynamics are addressed for the differential-difference equation ∈ẋ(t) + x(t) = f(x([t - k + 1])),0 < ∈ ≪ 1, where [̇] is the integer part function, k is a positive integer. The equation can be viewed as a special discretization (discrete version) of the singularly perturbed differential delay equation ∈ẋ(t) + x(t) = f(x(t - k)). Sufficient conditions for the invariance, existence, stability and shape of periodic solutions are derived. The principal analysis is based on reduction to special multi-dimensional maps whose relevant properties follow from those of 1D map f.

AB - Several aspects of dynamics are addressed for the differential-difference equation ∈ẋ(t) + x(t) = f(x([t - k + 1])),0 < ∈ ≪ 1, where [̇] is the integer part function, k is a positive integer. The equation can be viewed as a special discretization (discrete version) of the singularly perturbed differential delay equation ∈ẋ(t) + x(t) = f(x(t - k)). Sufficient conditions for the invariance, existence, stability and shape of periodic solutions are derived. The principal analysis is based on reduction to special multi-dimensional maps whose relevant properties follow from those of 1D map f.

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U2 - 10.1080/10236190902998008

DO - 10.1080/10236190902998008

M3 - Article

AN - SCOPUS:77951196619

VL - 16

SP - 157

EP - 171

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 2-3

ER -