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

Anatoli Ivanov, Eduardo Liz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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)).

Original languageEnglish (US)
Pages (from-to)137-145
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume180
Issue number1
DOIs
StatePublished - Aug 1 2005

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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