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.
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 language | English |
|---|---|
| Pages (from-to) | 99-109 |
| Number of pages | 11 |
| Journal | Electronic Journal of Differential Equations |
| Publication status | Published - 20 Nov 2015 |
| Event | 2014 Madrid Conference on Applied Mathematics - Universidad Politécnica de Madrid, Madrid, Spain Duration: 14 Jun 2014 → 15 Jun 2014 |
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.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.
Keywords
- pattern formation
- reaction-diffusion system