Resonant control of stochastic spatiotemporal dynamics in a tunnel diode by multiple time-delayed feedback

Abstract

We study the control of noise-induced spatiotemporal current density patterns in a semiconductor nanostructure (double-barrier resonant tunneling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of noise-induced oscillations compared to single time feedback, rendering the system more sensitive to variations in the delay time tau . The coherence of noise-induced oscillations measured by the correlation time exhibits sharp resonances as a function of tau , and can be strongly increased by optimal choices of tau . Similarly, the peaks in the power spectral density are sharpened. We provide analytical insight into the control mechanism by relating the correlation times and mean frequencies of noise-induced breathing oscillations to the stability properties of the deterministic stationary current density filaments under the influence of the control loop. Moreover, we demonstrate that the use of multiple time delays enlarges the regime in which the deterministic dynamical properties of the system are not changed by delay-induced bifurcations.

Control of Synchronization in Coupled Neural Systems by Time-Delayed Feedback

“…For increasing memory parame-ter R, the background becomes broader. We stress that a similar effect was found in the context of extended timedelayed feedback applied to the noise-induced oscillations in the Van-der-Pol system [Pomplun et al, 2007] and in a reaction-diffusion system [Majer & Schöll, 2009], where, in addition, the peaks become sharper.…”

Control of Complex Nonlinear Systems with Delay

“…For increasing memory parameter R, the background becomes broader. Let me stress that a similar effect was found in the context of extended time-delayed feedback applied to the noise-induced oscillations in the Van-der-Pol system [POM07] and in a reaction-diffusion system [MAJ09], where, in addition, the peaks become sharper. Before discussing the interspike interval distributions, let me consider the power spectra also in dependence on the coupling strength C and noise intensity D 1 for different memory parameters R. The reference cases in the absence of control can be found in Sections 6.2 as Figs.…”

Delay stabilization of periodic orbits in coupled oscillator systems

“…Delayed-feedback control, as proposed by Pyragas (1992), has proven to be a powerful non-invasive method for the stabilization of unstable periodic orbits (Schöll & Pyragas 1993;Baba et al 2002;Beck et al 2002;von Loewenich et al 2004) and unstable steady states (Hövel & Schöll 2005;Schikora et al 2006;Dahms et al 2007Dahms et al , 2008 in dynamical systems. It has, for instance, been successfully applied in spatially extended systems (Unkelbach et al 2003;Stegemann et al 2006;Postlethwaite & Silber 2007;Dahlem et al 2008, in press;Schneider et al 2009;Kyrychko et al in press) and even in noisedriven systems (Janson et al 2004;Pomplun et al 2005;Pototsky & Janson 2007;Prager et al 2007;Hizanidis & Schöll 2008;Majer & Schöll 2009). …”