### 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) |
---|---|

Pages (from-to) | 419-441 |

Number of pages | 23 |

Journal | Tohoku Mathematical Journal |

Volume | 54 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Tohoku Mathematical Journal*,

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

}

*Tohoku Mathematical Journal*, vol. 54, no. 3, pp. 419-441. https://doi.org/10.2748/tmj/1113247603

**Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations.** / Dormayer, Peter; Ivanov, Anatoli; Lani-Wayda, Bernhard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Floquet multipliers of symmetric rapidly oscillating solutions of differential delay equations

AU - Dormayer, Peter

AU - Ivanov, Anatoli

AU - Lani-Wayda, Bernhard

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036749506&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036749506&partnerID=8YFLogxK

U2 - 10.2748/tmj/1113247603

DO - 10.2748/tmj/1113247603

M3 - Article

VL - 54

SP - 419

EP - 441

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 3

ER -