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

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

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...

Full description

Bibliographic Details
Main Author: Michael Stich
Format: Article
Language:English
Published: Texas State University 2015-11-01
Series:Electronic Journal of Differential Equations
Subjects:
Pattern formation
reaction-diffusion system
control
Online Access:http://ejde.math.txstate.edu/conf-proc/22/s1/abstr.html
id doaj-7420da2572294e509f78668d153ad208
record_format Article
spelling doaj-7420da2572294e509f78668d153ad2082020-11-24T23:05:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-11-0120152299109Comments on multiple oscillatory solutions in systems with time-delay feedbackMichael Stich0 Aston Univ., Birmingham, UK 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, and 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.http://ejde.math.txstate.edu/conf-proc/22/s1/abstr.htmlPattern formationreaction-diffusion systemcontrol
collection DOAJ
language English
format Article
sources DOAJ
author Michael Stich
spellingShingle Michael Stich
Comments on multiple oscillatory solutions in systems with time-delay feedback
Electronic Journal of Differential Equations
Pattern formation
reaction-diffusion system
control
author_facet Michael Stich
author_sort Michael Stich
title Comments on multiple oscillatory solutions in systems with time-delay feedback
title_short Comments on multiple oscillatory solutions in systems with time-delay feedback
title_full Comments on multiple oscillatory solutions in systems with time-delay feedback
title_fullStr Comments on multiple oscillatory solutions in systems with time-delay feedback
title_full_unstemmed Comments on multiple oscillatory solutions in systems with time-delay feedback
title_sort comments on multiple oscillatory solutions in systems with time-delay feedback
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2015-11-01
description 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, and 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.
topic Pattern formation
reaction-diffusion system
control
url http://ejde.math.txstate.edu/conf-proc/22/s1/abstr.html
work_keys_str_mv AT michaelstich commentsonmultipleoscillatorysolutionsinsystemswithtimedelayfeedback
_version_ 1725626911498960896

Similar Items