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Frequency locking of modulated waves

Please always quote using this URN:urn:nbn:de:0296-matheon-6991
  • We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals.

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Metadaten
Author:Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky, Viktor Tkachenko, Serhiy Yanchuk
URN:urn:nbn:de:0296-matheon-6991
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/06/30
Release Date:2010/06/28
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C14 Symmetries, invariants
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C15 Nonlinear oscillations, coupled oscillators
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C29 Averaging method
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C60 Qualitative investigation and simulation of models
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D06 Synchronization
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D35 Stability of manifolds of solutions
Preprint Number:707
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