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 -