Extended time delayed feedback control of stochastic dynamics in a resonant tunneling diode
The influence of extended time delayed feedback upon the spatio-temporal current density patterns in a double barrier resonant tunnelling diode is investigated in a spatially extended model of this semiconductor nanostructure.
The parameters of the system are fixed at values below a Hopf bifurcation where the only stable state of the deterministic uncontrolled system is a spatially inhomogeneous "filamentary" steady state, and oscillating
space-time patterns do not occur.
The addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous self-sustained temporal oscillations. It has been shown that applying a single-time delayed feedback can either increase or
decrease the regularity of the noise-induced dynamics in this spatially extended system. We show that using multiple time delayed feedback provides means to increase the temporal regularity even further and enlarges the parameter regime in which no delay-induced bifurcations occur.
Using linear stability analysis the obtained results are explained in dependence of the delay time, the feedback strength and the memory parameter.