Comments on multiple oscillatory solutions in systems with time-delay feedback

Michael Stich

Research output: Contribution to journalArticle

Abstract

A complex Ginzburg-Landau equation subjected to local and global
time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the
disappearance of limit cycle solutions, derive analytical criteria for frequency
degeneration, amplitude degeneration, frequency extrema. Furthermore, we
discuss the influence of the phase shift parameter and show analytically that
the stabilization of the steady state and the decay of all oscillations (amplitude
death) cannot happen for global feedback only. Finally, we explain the onset
of traveling wave patterns close to the regime of amplitude death.
Original languageEnglish
Pages (from-to)99-109
Number of pages11
JournalElectronic Journal of Differential Equations
Publication statusPublished - 20 Nov 2015
Event2014 Madrid Conference on Applied Mathematics - Universidad Politécnica de Madrid, Madrid, Spain
Duration: 14 Jun 201415 Jun 2014

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Bibliographical note

Proceedings of the 2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal. Universidad Politécnica de Madrid, Madrid, Spain, June 14-15, 2014.

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Keywords

  • pattern formation
  • reaction-diffusion system

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