Time-Delay Feedback Control of an Oscillatory Medium
- The supercritical Hopf bifurcation is one of the simplest ways in which a stationary state of a nonlinear system can undergo a transition to stable self-sustained oscillations. At the bifurcation point, a small-amplitude limit cycle is born, which already at onset displays a finite frequency. If we consider a reaction-diffusion system that undergoes a supercritical Hopf bifurcation, its dynamics is described by the complex Ginzburg-Landau equation (CGLE). Here, we study such a system in the parameter regime where the CGLE shows spatio-temporal chaos. We review a type of time-delay feedback methods which is suitable to suppress chaos and replace it by other spatio-temporal solutions such as uniform oscillations, plane waves, standing waves, and the stationary state.
| Author details: | Michael Stich, Carsten BetaORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/978-3-030-16585-7_1 |
| ISBN: | 978-3-030-16585-7 |
| ISBN: | 978-3-030-16584-0 |
| ISSN: | 2199-3041 |
| ISSN: | 2199-305X |
| Title of parent work (English): | Biological Systems: Nonlinear Dynamics Approach |
| Publisher: | Springer |
| Place of publishing: | Cham |
| Publication type: | Other |
| Language: | English |
| Year of first publication: | 2019 |
| Publication year: | 2019 |
| Release date: | 2021/05/03 |
| Volume: | 20 |
| Number of pages: | 17 |
| First page: | 1 |
| Last Page: | 17 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
