A Study of the Effects of Spatially Localized Time-Delayed Feedback Schemes on Spatio-Temporal Patterns
Abstract
We present an investigation of two model systems: the Gray-Scott reaction-diffusion equation and the complex Ginzburg-Landau equation. 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 chaotic regimes. In these studies we have shown that selectively applying a time-delayed feedback scheme to a specific region of a chaotic system can generate periodic patterns that are distinct from those observed when controlling 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 02, 2022
- Accession Number
- AD1226327
Entities
People
- Jason E. Czak
Organizations
- Virginia Tech