### 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 language | English (US) |
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Pages (from-to) | 419-441 |

Number of pages | 23 |

Journal | Tohoku Mathematical Journal |

Volume | 54 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2002 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Dormayer, P., Ivanov, A. F., & Lani-Wayda, B. (2002). Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations.

*Tohoku Mathematical Journal*,*54*(3), 419-441. https://doi.org/10.2748/tmj/1113247603