TY  - GEN
A1  - Stich, Michael
A1  - Beta, Carsten
T1  - Time-Delay Feedback Control of an Oscillatory Medium
T2  - Biological Systems: Nonlinear Dynamics Approach
N2  - 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.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/50608
SN  - 978-3-030-16585-7
SN  - 978-3-030-16584-0
SN  - 2199-3041
SN  - 2199-305X
VL  - 20
SP  - 1
EP  - 17
PB  - Springer
CY  - Cham
ER  -