A study of the effects of spatially localized time-delayed feedback schemes on spatio-temporal patterns

In typical attempts to control spatio-temporal chaos, spatially extended systems were subjected to protocols that perturbed them as a whole, often overlooking the potential stabilizing interaction between adjacent regions. We have shown that through the application of a time-delayed feedback scheme to a specific localized region of a system periodic patterns can be generated that are distinct from those observed when controlling the whole system. In this thesis, we present the results of two interconnected studies: 1) Spatio-temporal patterns emerging from spatially localized time-delayed feedback perturbations within transient chaotic states of the Gray-Scott reaction-diffusion system 2) Spatio-temporal patterns emerging from spatially localized time-delayed feedback perturbations within chaotic states of the cubic complex Ginzburg-Landau equation We present an investigation of two model systems: the Gray-Scott reaction-diffusion equation and the complex Ginzburg-Landau equation. Specifically we numerically study two models characterized by exhibiting various chaotic regimes. We first consider a comprehensive study of the Gray-Scott model highlighting key details about different parameter space regimes and their relative proximity to the chaotic regime. Through a systematic investigation of the effects of the model control parameters, time-delayed feedback control strength parameters, perturbed region widths, and other quantities, we show that novel patterns can be formed through the appropriate choice of perturbation region and strength. For the second study we use spatially localized time-delayed feedback on the one-dimensional complex Ginzburg-Landau equation and demonstrate, through the numerical integration of the resulting real and imaginary equations, the stabilization of novel periodic patterns within three distinct chaotic regimes. In these studies we have shown that selectively applying a time-delayed feedback scheme to a specific spatially localized region of a chaotic system can bring forth periodic patterns that are distinct from those observed when applying a perturbation to the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. The mechanism underlying the observed pattern generation is related to the interplay between diffusion across the interfaces separating the different regions and time-delayed feedback. Research was sponsored by the Army Research Office and was accomplished under Grant No. W911NF-17-1-0156.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Department dc:contributor.department

Physics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Czak, Jason Edward

Chair dc:contributor.committeechair

• Pleimling, Michel Jean

Committee members dc:contributor.committeemember

• Cheng, Shengfeng
• Tauber, Uwe C.
• Piilonen, Leo E.

• non-equilibrium systems
• chaos
• control theory
• pattern formations

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:34450

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/110112