Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations

Peter Dormayer, Anatoli F. Ivanov, Bernhard Lani-Wayda

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Floquet multipliers of symmetric rapidly oscillating periodic solutions of the differential delay equation x(t) = αf(x(t), x(t − 1)) with the symmetries f(−x, y) = f(x, y) = −f(x,−y) are described in terms of zeroes of a characteristic function. A relation to the characteristic function of symmetric slowly oscillating periodic solutions is found. Sufficient conditions for the existence of at least one real multiplier outside the unit disc are derived. An example with a piecewise linear function f is studied in detail, both analytically and numerically.

Original languageEnglish (US)
Pages (from-to)419-441
Number of pages23
JournalTohoku Mathematical Journal
Volume54
Issue number3
DOIs
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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