Noise-induced pattern formation in a semiconductor nanostructure

Control of Timing Stability, and Suppression in Delayed Feedback Induced Frequency-Fluctuations by Means of Power Split Ratio and Delay Phase-Dependent Dual-Loop Optical Feedback

We experimentally demonstrated a power split ratio and optical delay phase dependent dual-loop optical feedback to investigate the suppression of frequency-fluctuations induced due to delayed optical feedback. The device under investigation is self-mode-locked (SML) two-section quantum-dash (QDash) laser operating at ∼21 GHz and emitting at ∼1.55 μm. The effect of two selective combinations of power split ratios (Loop-I: −23.29 dB and Loop-II: −28.06 dB, and Loop-I and Loop-II: −22 dB) and two optical delay phase settings ((i) stronger cavity set to integer resonance and fine-tuning the weaker cavity, (ii) weaker cavity set to integer resonance and fine-tuning of stronger cavity) on the suppression of cavity side-bands have been studied. Measured experimental results demonstrate that delayed optical feedback induced frequency-fluctuations can be effectively suppressed on integer resonance as well as on full delay range tuning (0–84 ps) by adjusting coupling strength −22 dB through Loop-I and Loop-II, respectively. Our findings suggest that power split ratio and delays phase-dependent dual-loop optical feedback can be used to maximize the performance of semiconductor mode-locked lasers.

Noise amplification in human tumor suppression following gamma irradiation

The influence of noise on oscillatory motion is a subject of permanent interest, both for fundamental and practical reasons. Cells respond properly to external stimuli by using noisy systems. We have clarified the effect of intrinsic noise on the dynamics in the human cancer cells following gamma irradiation. It is shown that the large amplification and increasing mutual information with delay are due to coherence resonance. Furthermore, frequency domain analysis is used to study the mechanisms.

Noise-controlled pattern formation and threshold shift for electroconvection in the conduction and dielectric regimes

We report noise-controlled electrohydrodynamic pattern formations and threshold shifts in nematic liquid crystals. In the electrohydrodynamic system superposed with noise, experimental results obtained in the dielectric regime are compared to those in the conventional conduction regime. The noise intensity dependences of thresholds and pattern evolution processes are remarkably different for each regime. The pattern formation mechanisms in the presence of noise for both regimes are discussed based on the results. Moreover, it is found that the thresholds and characteristic wavelengths of dissipative structures can be effectively controlled by external multiplicative noises with appropriate intensity and correlation times.

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

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.

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

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.

Suppressing noise-induced intensity pulsations in semiconductor lasers by means of time-delayed feedback

We investigate the possibility to suppress noise-induced intensity pulsations (relaxation oscillations) in semiconductor lasers by means of a time-delayed feedback control scheme. This idea is first studied in a generic normal-form model, where we derive an analytic expression for the mean amplitude of the oscillations and demonstrate that it can be strongly modulated by varying the delay time. We then investigate the control scheme analytically and numerically in a laser model of Lang-Kobayashi type and show that relaxation oscillations excited by noise can be very efficiently suppressed via feedback from a Fabry-Perot resonator.

Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation

Here we address the effect of large delay on the statistical characteristics of noise-induced oscillations in a nonlinear system below Andronov-Hopf bifurcation. In particular, we introduce a theory of these oscillations that does not involve the eigenmode expansion, and can therefore be used for arbitrary delay time. In particular, we show that the correlation matrix (CM) oscillates on two different time scales: on the scale of the main period of noise-induced oscillations, and on the scale close to the delay time. At large values of the delay time, the CM is shown to decay exponentially only for large values of its argument, while for the arguments comparable with the value of the delay, the CM remains finite disregarding the delay time. The definition of the correlation time of the system with delay is discussed.

Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode

The influence of time-delayed feedback upon the spatiotemporal current density patterns is investigated in a model of a semiconductor nanostructure, namely a double-barrier resonant tunneling diode. The parameters are chosen below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. The addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous self-sustained temporal oscillations that can be quite coherent. We show that applying a time-delayed feedback can either increase or decrease the regularity of the noise-induced dynamics in this spatially extended system. Using linear stability analysis, we can explain these effects, depending on the length of the delay interval. Furthermore, we study the influence of this additional control term upon the deterministic behavior of the system, which can change significantly depending on the choice of parameters.