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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:180

Article

Ivanov, A ; Liz, E

关键词: singular differential delay equations;    limiting difference equations;    continuous dependence on parameters;    periodic solutions;    Farey-type nonlinearity;    one-dimensional maps;    globally attracting cycles;   

DOI  :  10.1016/j.cam.2004.10.006

来源: Elsevier

【 摘 要 】

We address the problem of existence of periodic solutions for the differential delay equation epsilon x(t) + x(t) = f(x(t - 1)), 0 < epsilon << 1, with the Farey nonlinearity f(x) of the form f(x) = mx + A if x <= 0, mx - B if x > 0, where vertical bar m vertical bar < 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 epsilon -> 0(+)) difference equation x(t) = f(x(t - 1)). (c) 2004 Elsevier B.V All rights reserved.

【 授权许可】

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