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Spatiotemporal patterns emerging from a spatially localized time-delayed feedback scheme
Jason Czak1,2, Michel Pleimling1,2,3
1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.
Physical Review. E
|January 15, 2022
Summary
Selectively controlling parts of complex systems, rather than the whole, can create novel space-time patterns. This localized feedback method stabilizes periodic patterns in reaction-diffusion systems.
Area of Science:
- Complex systems dynamics
- Nonlinear dynamics
- Pattern formation
Background:
- Managing spatiotemporal chaos in extended systems often involves global perturbations.
- Previous methods aimed to stabilize entire systems into uniform states.
Purpose of the Study:
- To investigate if localized perturbations can generate unique space-time patterns.
- To explore pattern emergence in both perturbed and unperturbed regions.
Main Methods:
- Applied a spatially localized time-delayed feedback scheme.
- Utilized the one-dimensional Gray-Scott reaction-diffusion system.
- Performed numerical integration of kinetic equations.
Main Results:
- Demonstrated the stabilization of spatially localized, perfectly periodic space-time patterns.
- Observed pattern generation in both perturbed and unperturbed regions.
- Identified diffusion across region interfaces as a key mechanism.
Conclusions:
- Localized control offers a novel approach to pattern generation in complex systems.
- Selective perturbation can yield patterns unattainable through global control.
- Diffusion dynamics play a crucial role in localized pattern formation.
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