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

Stich, Michael (2015). Comments on multiple oscillatory solutions in systems with time-delay feedback. Electronic Journal of Differential Equations , pp. 99-109.

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.

Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: Proceedings of the 2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal. Universidad Politécnica de Madrid, Madrid, Spain, June 14-15, 2014. This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author.
Uncontrolled Keywords: pattern formation,reaction-diffusion system
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Published Date: 2015-11-20
Authors: Stich, Michael ( 0000-0001-8862-1044)

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