Noise-Induced Front Motion: Signature of a Global Bifurcation

Abstract

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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;).…”

Lyapunov stability of charge transport in miniband semiconductor superlattices

“…[23][24][25]37 They are able to demonstrate negative differential conductance, 23,37 which induces new regimes of collective charge transport accompanied by rich instability phenomena. 5,6,[38][39][40][41][42] The collective dynamics of miniband electrons 6,25 can be described by the one-dimensional (1D) current continuity equation…”

Regularization of chaos by noise in electrically driven nanowire systems

“…There have also been recent works on coherence resonance in nanoscale systems [49][50][51]. In particular, coherence resonance in a single-walled Carbon nanotube ion channel was uncovered [49].…”

“…It was found [50] that the regularity of the spatial distribution of pores in a nanostructure can be maximized by some optimal level of internal noise. It was also discovered [51] that the electron dynamics in a semiconductor superlattice can exhibit coherence resonance. In these works, the intrinsic dynamics of the nanoscale systems were regular, and the systems were assumed to be in low-temperature environment.…”

“…Physically, as compared with the existing works in Refs. [49][50][51], the distinct features of our present work are twofold: (1) we study the parameter regime where the deterministic dynamics are chaotic and motivate our work from the perspective of control, and (2) we assume that the operational environment of the nanowire is under room conditions. The issue of chaos control is challenging, as existing methods cannot be extended to the nanowire system.…”