Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

The diffusion in a harmonic oscillator driven by coloured noises $\xi(t)$ and $\eta(t)$ with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time $\tau_3$ exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient $\lambda$ of the two Ornstein--Uhlenbeck (O-U) noises. 2) Changing the value of $\tau_3$, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.     

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w(z) and the power in the bucket (PIB) are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity I_max and the PIB decrease and w(z) increases as the refraction index structure constant C_n² increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance x_d and beam number M is less affected by the turbulence than that with a larger value of γ and smaller values of x_d and M. The main results obtained in this paper are explained physically.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times

We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity , the variance, λ_2(0), and the skewness,λ_3(0) of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized.     

Influences of Modulated Noise on Normalized Intensity Fluctuation in a Single-Mode Laser

The influences of the two forms of modulated noises,i.e.the bias signal-modulated noise and the direct signalmodulated noise,on the normalized intensity fluctuation (NIF) are investigated,and the results of the two forms of modulation are compared in detail,We find that a minimum for the case of the bias signal modulation appears in the curve of the dependence of the NIF upon the quantum and pump noise intensities when the correlation coefficient between the quantum noise and the pump noise is negative.However,the NIF for the case of the direct signal modulation is independent of the correlation coefficient between the two noises.Moreover,at the same parameter region,the NIF for the bias signal modulation is only one-eighth as much as.that for the direct signal modulation.     

Paraxial propagation of cosh-Airy vortex beams in chiral medium

Propagation dynamics of the cosh-Airy vortex(CAiV) beams in a chiral medium is investigated analytically with Huygens–Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polarized vortex(LCPV) beams and the right circularly polarized vortex(RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams.The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe's intensity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe's intensity and peak intensity become larger. Besides, the main lobe's intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther propagation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe's intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.     

Stochastic Resonance in an Asymmetric Bistable System Subject to Frequency Mixing Periodic Force and Noise

The phenomenon of stochastic resonance (SR) in an asymmetric bistable system subject to the multiplicative and additive white noises and two periodic fields is investigated. Using the two-state theory, analytic expressions of the signal-to-noise ratio (SNR) for fundamental harmonics and higher harmonics are derived. It is found that SR appears at both fundamental harmonics and mixed harmonics (of second- and third-order approximation).Moreover, the higher the order of mixed harmonics is, the larger the SNR values are. The effects of static asymmetry on the SNR (of second- and third-order approximation) are different, and the noise intensity ratio can enhance the SNR for higher harmonics.     

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time (MFPT) and the spectral power amplification (SPA) are obtained, respectively. Based on the numerical computations, it is found that: (i) The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises (λ>0), this maximum for MFPT shows the characteristic of the entropic noise induced stability (ENIS) effect. The intensity λ of correlations between two noises can enhance the ENIS effect. (ii) The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh--Rose (H--R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D’, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.     

Effects of Levy noise and immune delay on the extinction behavior in a tumor growth model

The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.     

Effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model

The combined effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model are explored. The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α < 1, but inhibits tumor extinction when the stability index α > 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.     

Spectrum analysis of all parameter noises in repetition-rate laser pulse train

The theoretical investigation of all parameter noises in repetition-rate laser pulse train was presented. The expression of power spectrum of laser pulse trains with all parameter noises was derived, and the power spectra of pulse trains with different noise parameters were numerically simulated. By comparing the power spectra with and without pulse-width jitter, we noted that pulse-width jitter could not be neglected compared with amplitude noise and timing jitter and contributed a great amount of noise into the power spectrum under the condition that the product of pulse width and angular frequency was larger than 1.     

Spectrum analysis of all parameter noises in repetition-rate laser pulse train

The theoretical investigation of all parameter noises in repetition-rate laser pulse train was presented. The expression of power spectrum of laser pulse trains with all parameter noises was derived, and the power spectra of pulse trains with different noise parameters were numerically simulated. By comparing the power spectra with and without pulse-width jitter, we noted that pulse-width jitter could not be neglected compared with amplitude noise and timing jitter and contributed a great amount of noise into the power spectrum under the condition that the product of pulse width and angular frequency was larger than 1.     

Low-frequency fluctuation in multimode semiconductor laser subject to optical feedback

Dynamics of a semiconductor laser subject to moderate optical feedback operating in the low-frequency fluctuation regime is numerically investigated.Multimode Lang-Kobayashi(LK)equations show that the low-frequency intensity dropout including the total intensity and sub-modes intensity is accompanied by sudden dropout simultaneously,which is in good agreement with experimental observation.The power fluctuation is quite annoying in practical applications,therefore it becomes important to study the mech- anism of power fluctuation.It is also shown that many factors,such as spontaneous emission noise and feedback parameter,may influence power fluctuation larger than previously expected.     

A unified drain current 1/f noise model for GaN-based high electron mobility transistors

In this work, we present a theoretical and experimental study on the drain current 1/f noise in the AIGaN/GaN high electron mobility transistor （HEMT）. Based on both mobility fluctuation and carrier number fluctuation in a two- dimensional electron gas （2DEG） channel of AlGaN/GaN HEMT, a unified drain current 1/f noise model containing a piezoelectric polarization effect and hot carrier effect is built. The drain current 1/f noise induced by the piezoelectric polarization effect is distinguished from that induced by the hot carrier effect through experiments and simulations. The simulation results are in good agreement with the experimental results. Experiments show that after hot carrier injection, the drain current 1/f noise increases four orders of magnitude and the electrical parameter degradation Agm/gm reaches 54.9%. The drain current 1/f noise degradation induced by the piezoelectric effect reaches one order of magnitude; the electrical parameter degradation Agm/gm is 11.8%. This indicates that drain current 1/f noise of the GaN-based HEMT device is sensitive to the hot carrier effect and piezoelectric effect. This study provides a useful reliability characterization tool for the A1GaN/GaN HEMTs.     

Propagation of phase-locked truncated Gaussian beam array in turbulent atmosphere

Truncation manipulation is a simple but effective way to improve the intensity distribution properties of the phase-locked Gaussian beam array at the receiving plane. In this paper, the analytical expression for the propagation of the phase-locked truncated Gaussian beam array in a turbulent atmosphere is obtained based on the extended Huygens--Fresnel principle. Power in the diffraction-limited bucket is introduced as the beam quality factor to evaluate the influence of different truncation parameters. The dependence of optimal truncation ratio on the number of beamlets, the intensity of turbulence, propagation distance and laser wavelength is calculated and discussed. It is revealed that the optimal truncation ratio is larger for the laser array that contains more lasers, and the optimal truncation ratio will shift to a larger value with an increase in propagation distance and decrease in intensity of atmosphere turbulence. The optimal truncation ratio is independent of laser wavelength.     

Effect of Time Delay on Binary Signal Detection via a Bistable System

The effect of time delay on binary signal detection via a bistable system in the presence of white or colored Gaussian noise is investigated. By defining the bit error rate based on the solution of the approximated Fokker- Planck equation, the detector performance is investigated theoretically and is verified by Monte Carlo simulation. It is shown that, when the system parameter or noise intensity is optimally chosen, the increasing time delay generally improves the system performance. It is also shown that it is more difficult to accurately predict the system performance with a larger time delay and correlation time. This may inspire more thorough investigations in cooperative effects of a nonlinear system and time delay on signal processing.