Control of noise‐induced spatiotemporal patterns in superlattices

Abstract

We investigate a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts (travelling field domains) in the presence of noise and control. In the uncontrolled system noise is able to induce electron charge front motion through the device when the system is prepared near a global bifurcation which yields it highly sensitive to fluctuations. The associated current density oscillations exhibit a maximum of coherence at an optimal noise intensity, a phenomenon known as coherence resonance. We show how control in the form of a time‐delayed feedback signal affects the noise‐induced dynamics. We observe that control induces a limit cycle in a wide range of the control parameter space and therefore destroys the effect of coherence resonance. For low noise intensity, time‐delayed feedback control enhances the regularity (coherence) of the noisy oscillations considerably. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Complex Dynamics of Semiconductor Quantum Dot Lasers Subject to Delayed Optical Feedback

“…4(e)] scales logarithmically with the distance from the bifurcation point k bif = 0.096. This behavior is typical for a homoclinic bifurcation of limit cycles with a negative saddle quantity [Kuznetsov, 1995;Hizanidis & Schöll, 2008]. The saddle quantity for a saddle-focus is defined as σ 0 := λ s + (λ u,± ), where λ s is the positive real eigenvalue and (λ u,± ) are the real parts of the complex conjugate leading eigenvalues, respectively.…”

Time-delayed feedback in neurosystems

“…One could also consider the application of the feedback scheme to both subsystems and the effects of different values of the control parameters for each subsystem, but these investigations are beyond the scope of this work. Previously, time-delayed feedback has also been used to influence noise-induced oscillations of a single excitable system Janson et al 2004;Prager et al 2007), of systems below a Hopf bifurcation (Pomplun et al 2005;Schöll et al 2005;Flunkert & Schöll 2007;Pototsky & Janson 2007) or below a global bifurcation (Hizanidis et al 2006;Hizanidis & Schöll 2008) and of spatially extended reactiondiffusion systems Stegemann et al 2006;Dahlem et al 2008). Extensions to multiple time-delay control schemes have also been considered (Hövel et al 2007, submitted;Pomplun et al 2007;).…”

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

“…This method has been widely used with great success in problems in physics, chemistry, biology, and medicine [15] including reaction-diffusion systems [29,30,31,32,33]. In particular, it was demonstrated that it can be used to control the coherence and the timescales of noise-induced oscillations in a single FHN system [34,35,36] and in two coupled excitable FHN systems [37,38] as well as noise-induced patterns in reaction-diffusion systems [39,40,41,42] and wave propagation in excitable media [43]. This motivates our efforts to investigate whether a failure of such an intrinsic noninvasive control scheme can explain the onset of excitation spread in a spatially continuous FHN systems as a model of spreading pathological processes in the cortex during migraine and stroke.…”