TY - JOUR

T1 - Periodic solutions of a singular differential delay equation with the Farey-type nonlinearity

AU - Ivanov, Anatoli

AU - Liz, Eduardo

N1 - Funding Information:
We started to write the paper while A. Ivanov was visiting the University of Vigo under the support of a grant from the Xunta de Galicia (Spain). He is thankful to both institutions for their support and hospitality.
Funding Information:
This research was supported in part by the NSF Grant INT 0203702 (USA) (A. Ivanov), and by M. C. T. (Spain) and FEDER under project BFM2001-3884 (E. Liz).

PY - 2005/8/1

Y1 - 2005/8/1

N2 - We address the problem of existence of periodic solutions for the differential delay equation εẋ(t) + x(t) = f(x(t - 1)), 0 < ε≪ 1, with the Farey nonlinearity f(x) of the form f(x) = {mx-Bifx>0, {mx+Aifx≤0 where m < 1, A > 0, B > 0. We show that when the map x → f(x) has an attracting 2-cycle then the delay differential equation has a periodic solution, which is close to the square wave corresponding to the limit (as ε → 0+) difference equation x(t) = f(x(t - 1)).

AB - We address the problem of existence of periodic solutions for the differential delay equation εẋ(t) + x(t) = f(x(t - 1)), 0 < ε≪ 1, with the Farey nonlinearity f(x) of the form f(x) = {mx-Bifx>0, {mx+Aifx≤0 where m < 1, A > 0, B > 0. We show that when the map x → f(x) has an attracting 2-cycle then the delay differential equation has a periodic solution, which is close to the square wave corresponding to the limit (as ε → 0+) difference equation x(t) = f(x(t - 1)).

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U2 - 10.1016/j.cam.2004.10.006

DO - 10.1016/j.cam.2004.10.006

M3 - Article

AN - SCOPUS:17644399819

SN - 0377-0427

VL - 180

SP - 137

EP - 145

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -