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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 54 NO.3 / (2002))
Floquet Multipliers of Symmetric Rapidly Osicllating Solutions of Differential Delay Equations
Peter Dormayer, Anatoli F. Ivanov, Bernhard Lani-Wayda,
Pages. 419-441
Abstract Floquet multipliers of symmetric rapidly oscillating periodic solutions of
the differential delay equation $dot{c}(t)= alpha f(x(t), x(t-1))$ 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.
Contents 1. Introduction
2. Rapidly oscillating periodic solutions and transformations
3. Characteristic functions
4. Multipliers of rapidly and slowly oscillating solutions
5. A specific example with piecewise linear feedback
Key words Delay equations with symmetry, rapidly oscillating periodic solutions, stability, Floquet multipliers
Mathmatical Subject Classification 34K13, 34K18