Periodic solutions of a discretized differential delay equation

Anatoli F. Ivanov, Sergei I. Trofimchuk

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)157-171
Number of pages15
JournalJournal of Difference Equations and Applications
Issue number2-3
StatePublished - Feb 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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