TY - CHAP
T1 - Time-delay feedback control of an oscillatory medium
AU - Stich, Michael
AU - Beta, Carsten
PY - 2019/4/30
Y1 - 2019/4/30
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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85065446320&partnerID=8YFLogxK
UR - https://link.springer.com/chapter/10.1007%2F978-3-030-16585-7_1
U2 - 10.1007/978-3-030-16585-7_1
DO - 10.1007/978-3-030-16585-7_1
M3 - Chapter
AN - SCOPUS:85065446320
SN - 978-3-030-16584-0
T3 - SEMA SIMAI Springer Series
SP - 1
EP - 17
BT - SEMA SIMAI Springer Series
A2 - Landeira, J.
A2 - Escribano, B.
PB - Springer
ER -