Effects of Time Delay on the Bistable System Subjected to Correlated Noises

The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function （SPDF） is derived, and under the condition of large delay time, the SPDF is stochastically simulated. The analytical and simulative results indicate that： （i） For the case of λ = 0 （λ denotes the strength of correlations between the multiplicative and additive noises）, the time delay affects weakly the SPDF peak structure, and the symmetrical property of the SPDF two-peak structure does not change with the increasing delay time. （ii） For the case of λ≠0, the two-peak structure changes with the increasing delay time, i.e. one peak goes up and the other go down simultaneously as the delay time increases and along with further increase of the delay time, the lower peak disappears gradually while the higher one goes up, i.e. the structure of the SPDF changes from a bimodal to a unimodal and the system becomes monostable.     

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises： Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.     

Coherence Resonance in the System with Periodical Potential and Driven by Correlated Noises

We study the ratchet model with both thermal and potential fluctuations, discussing analytically the coherence resonance of the particle moving in such a potential field. It is found that the correlation between the thermal and potential fluctuations has significant effect on the coherence of the system, i.e. negative correlation enhances the coherence of the system greatly, and with positive correlation, there appears the phenomenon that the coherence suppression and enhancement occur alternatively as the additive noise becomes larger.     

Experimental Analysis of Stochastic Resonance in a Duffing System

An experimental circuit is used to study the stochastic resonance(SR) phenomena in a Duffing system.The charcacteristics of SR are investigated from various aspects by varying all the possible parameters,The deviations between the experimental results and the adiabatic theory are presented.     

Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.     

Correlated Noises in a Prey-Predator Ecosystem

We investigate a Volterra ecosystem driven by correlated noises. The fluctuation in the death rate of the predator induces an increase of population density of the predators. The fluctuation in the growth rate of the prey, however, leads the predators to decay. It is reported that the predators undergo sensitivity to a random environment, whereas the preys exhibit a surprising endurance to the same stochastic factor. The predators are of better stability under strong correlation of noises.     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.     

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.     

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.     

Stochastic Resonance in a Bistable Sawtooth Potential Driven by COrrelated Multiplicative and Additive Noise

We Present and analytical investigation of the signal-to-noise ratio(SNR)by studying the bistable sawtooth system driven by correalted Gaussian white noise.The analytic expression of the SNR is obtained.We detect some novel results,as follows.(1) Stochastic resonance(SR) always occurs in the SNR-Q (the multiplicative noise intensity)curve for the whole range of correlation coefficients.(2)There is not only resonance but also suppression and monotony in the dependence of SNR upon the additive noise intensity.(3) There are two extrema(one is minimum,the other meximum)in the SNR-b(the barrier height)curve for different multiplicative noise intensities.     

Stochastic Resonance in an Over-Damped Bias Linear System with Dichotomous Noise

The stochastic resonance in an over-damped bias linear system subject to multiplicative and additive dichotomous noise （DN） is investigated. By using the linear-response theory and the properties of the DN, the exact expressions are found for the signal-to-noise ratio （SNR）. It is shown that the SNR is a non-monotonic function of the correlation time of the additive DN, and it varies non-monotonically with the bias of the external field, the intensity and asymmetry of the multiplicative DN, as well as the external field frequency. Moreover, the SNR depends on the bias of the system, as well as the strength and asymmetry of the additive DN.     

Stochastic Resonance in Linear Region of a Single-Mode Laser： Effects of Amplitude Modulation of Signal

A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross-correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance (SR) respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model: the conventional form of SR, the SR in the broad sense, and the bona fide SR.     

Suprathreshold Stochastic Resonance in a Single Comparator

Stochastic resonance usually appears when stimulus is too weak to overcome barriers in a nonlinear system. Unusually, we demonstrate that in a simple competitor as a prototype model, stochastic resonance can still occur when the stimulus is predominantly suprathreshold. This result provides new knowledge for understanding of mechanism underlying information process in biological systems and aIso finds appfications in signal processing.     

The Fiber Soliton Communication System with Stochastic Variation of Gain

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Influence of Delayed-Time and Colored-Noise in a Bistable System Subject to Asymmetric Dichotomous Noise and Colored Noise

The influence of delayed-time and colored-noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied. Applying small delay-time approximation, under the adiabatic limit condition, the expression of the signal-to-noise ratio (SNR) of the system is obtained. It is found that, the SNR varies non-monotonously with the delayed-time and the correlation of the colored noise. Moreover, the SNR exhibits SR behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise, and as a function of the strength of the colored noise.     

Stochastic Resonance in Neural Systems with Small-World Connections

We study the stochastic resonance （SR） in Hodgkin-Huxley （HH） neural systems with small-world （SW） connections under the noise synaptic current and periodic stimulus, focusing on the dependence of properties of SR on coupling strength c. It is found that there exists a critical coupling strength c^＊ such that if c 〈 c^＊, then the SR can appear on the SW neural network. Especially, dependence of the critical coupling strength c^＊ on the number of neurons N shows the monotonic even almost linear increase of c^＊ as N increases and c^＊ on the SW network is smaller than that on the random network. For the effect of the SW network on the phenomenon of SR, we show that decreasing the connection-rewiring probability p of the network topology leads to an enhancement of SR. This indicates that the SR on the SW network is more prominent than that on the random network （p = 1.0）. In addition, it is noted that the effect becomes remarkable as coupling strength increases. Moreover, it is found that the SR weakens but resonance range becomes wider with the increase of c on the SW neural network.     

Dispersion and Collapse in Stochastic Velocity Fields on a Cylinder

The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is such that when the radius of the cylinder tends to infinity the fluid particles separate in an explosive way. Nevertheless, when the radius is finite the transition probability of the two-particle separation converges to an invariant measure. This behavior is due to the large-scale compressibility generated by the compactification of one dimension of the space.     

The Influence of Dispersion Stochastic Variation on Bright Soliton Transmision System

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Effects of Cross-Correlation Colour Noises on Tumour Growth Process

We present a tumour cell growth process model including a multiplicative coloured noise and an additive coloured noise correlated. How the noise cross-correlation intensity λ and correlation time T can affect the steady state properties of tumour cell growth model are discussed by solving an approximative Fokker-Planck equation. It is found that the increase of noise correlation time T can cause the tumour cell number increasing, but the increase of multiplicative noise intensity can cause the tumour cell number extinction. We also find that the increase of cross-correlation intensity λ in the case of 0 〈 λ 〈 1 can cause the tumour cell number extinction, whereas increase of cross-correlation intensity λ in the case of λ 〈 0 can cause the tumour cell number increasing.