TY - JOUR

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

AU - Dormayer, Peter

AU - Ivanov, Anatoli F.

AU - Lani-Wayda, Bernhard

PY - 2002

Y1 - 2002

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.

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U2 - 10.2748/tmj/1113247603

DO - 10.2748/tmj/1113247603

M3 - Article

AN - SCOPUS:0036749506

VL - 54

SP - 419

EP - 441

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 3

ER -