Transient behavior in systems with time-delayed feedback

Abstract

We investigate the transient times for the onset of control of steady states by time-delayed feedback. The optimization of control by minimizing the transient time before control becomes effective is discussed analytically and numerically, and the competing influences of local and global features are elaborated. We derive an algebraic scaling of the transient time and confirm our findings by numerical simulations in dependence on feedback gain and time delay.