Stochastic resonance driven by time-modulated correlated coloured noise sources in a single-mode laser

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ1, τ2 and cross-correlated time τ3 for stochastic resonance are analysed in two ways： τ1, τ2 and τ3 are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient F and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Г.

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio （SNR） of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.

Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.

Formation and instability of spiral wave induced by Gaussian coloured noise

In this paper, we studied the effect of Gaussian coloured noise on the formation and instability of spiral waves described by one class of modified FitzHugh Nagumo equation. It was found that Gaussian coloured noise plays a constructive role in the formation, transition and instability of spiral wave. Too weak or too strong noise may act against the formation of spiral waves. At a certain noise level, spiral wave is maintained in a medium, in which spiral wave cannot be observed in the absence of the noise. It is difficult to make a stable spiral wave into unstable state by Gaussian coloured noise, unless the noise level is very high. The parameter regions of Gaussian coloured noise for spiral forming and spiral instability were given and discussed with numerical simulations.

BDS/GPS deformation analysis of a long-span cable-stayed bridge based on colored noise filtering

Combining GPS and BDS technology to monitor the deformation of long-span railway bridges with stricter deformation control requirements is of significance to the safety and control of the bridge and the safety of railway traffic.Previous studies have ignored the influence of coloured noise in the deformation time series.This is not conducive to accurate deformation analysis of long-span railway bridges.Therefore,GPS,BDS and GPS/BDS monitoring data of Ganjiang Bridge located in Ganzhou city,Jiangxi Province,China are adopted in this paper to filter the coloured noise in the deformation time series by principal component analysis(PCA),and the influence of coloured noise on the deformation analysis results of railway bridge is analysed.The experimental results show that the diurnal temperature difference causes the mid-span and the tower of the railway cable-stayed bridge to deform with a period of about one day in the vertical and longitudinal directions,respectively.Ignoring colored noise will make the uncertainty of the deformation parameter estimation overly optimistic.PCA can significantly reduce the coloured noise,and thus reduce the uncertainty of deformation parameter estimation by about 73%.Moreover,the average difference between the daily periodic motion amplitudes of the monitoring points obtained by using GPS and BDS deformation time series is 1.65 mm.The use of GPS/BDS deformation time series is not only helpful to reduce the influence of coloured noise,but also can reduce the difference between amplitude analysis results obtained from GPS and BDS deformation time series.

Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time τ1 and τ2 by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. （1） The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate μ decides that the selection is propitious to gene A haploid or gene B haploid. （2） The additive coloured noise intensity and the correlation time τ2 play opposite roles. It is noted that α and τ2 can not separate the single peak, while can make the peak disappear and ^-2 can make the peak be sharp. （3） The multiplicative coloured noise intensity D and the correlation time τ1 can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing D and decreasing τ1.