Evidence of parameter-induced aperiodic stochastic resonance with fixed noise

Stochastic resonance (SR) is based on the cooperative effect between the stochastic dynamical system and the external forcing. As is well known, the cooperative effect is produced by adding noises. In this paper, we show the evidence that by changing the system parameters and the signal intensity, a nonlinear system in the presence of an input aperiodic signal can yield the cooperative effect, with the noise fixed. To quantify the nonlinear system output, we determine the theoretical bit error rate (BER). By numerical simulation, the validity of the theoretical derivation is checked. Besides, we show that parameter-induced SR is more realizable than SR via adding noises, especially when the noise intensity exceeds the resonance level, or when the characteristic of the noise is not known.     

Generalized Fokker-Planck equation: Derivation and exact solutions

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise, and show that it reproduces all Fokker-Planck equations that are known for these noises. Exact analytical, time-dependent and stationary solutions of the generalized Fokker-Planck equation are derived and analyzed in detail for the cases of a linear, a quadratic, and a tailored potential.     

乘性噪音和加性噪音效应对脉孢菌生物钟体系内信号随机共振的增强

利用有和无外信号作用的脉孢菌生物钟体系,研究了与加性噪音相关或不相关的乘性噪音对加性噪音诱导出的内信号随机共振的影响作用.结果表明：无外信号的情况下,不论加性和乘性噪音相关与否,当乘性噪音强度小于临界值时,乘性噪音的加入使加性噪音诱导产生的内随机共振强度得到增强;当大于其临界值时,加性噪音的随机共振强度却得不到进一步增强,这说明脉孢菌生物钟体系能抵抗外噪音的干扰而维持自身的生理节奏.当加入外信号时,对于乘性和加性噪音不相关的情况,发现存在最佳频率（0.003 Hz）的外信号能使加性噪音诱导出的内信号随机共 关键词： 噪音 脉孢菌生物钟体系 内信号随机共振     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.     

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance.     

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.     

A random walker on a ratchet potential: effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.     

An adaptive speech enhancement method for siren noise cancellation

Siren noises usually severely disturb the intelligibility of voice communication inside the cabs of police, paramedic and fire vehicles. It is often desired that such unwanted noise can be removed from the speech signal. In this paper, a new method is proposed to adaptively cancel siren noises and enhance speech signals. Based on the characteristics of siren noises, an anti-speech filter and a time delayer are employed in the single and dual channel noise cancellation systems to reduce the siren noises. Experiment results demonstrate that the effectiveness of the proposed method for canceling the siren noises and the performance of the enhanced speech signal is satisfying.     

Entropic stochastic resonance: the constructive role of the unevenness

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties.     

Nonstationary stochastic resonance viewed through the lens of information theory

In biological systems, information is frequentlytransferred with Poisson like spike processes (shot noise) modulatedin time by information-carrying signals. How then to quantifyinformation transfer by such processes for nonstationary inputsignals of finite duration? Is there some minimal length of theinput signal duration versus its strength? Can such signals bebetter detected when immersed in noise stemming from thesurroundings by increasing the stochastic intensity? These are somebasic questions which we attempt to address within an analyticaltheory based on the Kullback-Leibler information concept applied torandom processes.     

Stochastic resonance in finite arrays of bistable elements with local coupling

In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective variable. By means of numerical simulations, the signal-to-noise ratio (SNR) and the gain are estimated as functions of the noise and the interaction coupling strength. A strong enhancement of the SR phenomenon for this collective variable in comparison with SR in single unit bistable systems is observed. Gains larger than unity are obtained for some parameter values and multi-frequency driving forces, indicating that the system is operating in a non-linear regime albeit the smallness of the driving amplitude. The large SNR values observed are basically due to the fact that the output fluctuations are small and short lived, in comparison with their typical values in a linear regime. A non-monotonic behavior of the SNR with the coupling strength is also obtained.     

具有色关联的色噪声驱动下单模激光线性模型的随机共振

研究了具有指数形式关联的两色噪声驱动下单模激光线性模型受信号调制后其输出信噪比，发现了随机共振现象.根据计算结果讨论了噪声（即噪声强度、噪声间互关联程度和关联时间）和信号（信号频率和信号振幅）对信噪比的影响. 关键词： 随机共振 噪声关联时间 信噪比     

Stochastic resonance: influence of a f-κ noise spectrum

With the aim of studying stochastic resonance (SR) in a double-well potential when the noise source has a spectral density of the form f^-κ (with varying κ), we have extended a procedure introduced by Kaulakys et al. (Phys. Rev. E 70, 020101 (2004)). In order to achieve an analytical understanding of the results, we have obtained an effective Markovian approximation that allows us to make a systematic study of the effect of such noise on the SR phenomenon. A comparison of the numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.     

Colored Gaussian noises induced stochastic resonance and stability transition for an insect growth system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady-state shift behaviors and the stochastic resonance phenomenon (SR) for a biological insect population system with a multiplicative periodic signal caused by the terms of the colored multiplicative and additive noises. Our research results imply that the multiplicative noise and the self-correlation of the additive noise can weaken the stability of the biological system and restrain the growth of the insect population, while the additive noise and the self-correlation time of the multiplicative noise can strengthen the stability of the insect system and facilitate the biological population to breed. As regards to the phenomenon of the SR evoked by a multiplicative periodic signal, noise terms and their correlation times, the computed results show that the additive noise intensity M and the self- correlation time τ₁ of the multiplicative noise can both improve the SR effect. Inversely, the multiplicative noise intensity Q and the self-correlation time τ₂ of the additive noise can suppress together the SR phenomenon. Whereas, it should be pointed out that in the SNR-Q and SNR-M plots, the two self-correlation times can both motivate a resonant peak, but not change the peak value of the SNR no matter how the two noise correlation times vary.     

关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

Delay induced steady-state transition and stochastic resonance for an ecological vegetation growth system subjected to multiplicative and additive noises

In this paper, our aim is to investigate the steady state properties and stochastic resonance (SR) phenomenon for an ecological vegetation growth system with time delay induced by the multiplicative and additive noises. Numerical results show that the SR phenomenon caused by time delay, different noise terms and a weak periodic signal occurs in the vegetation growth model under different values of system parameters. With regard to the stationary state properties of the vegetation system, the results indicate that the terms of different noises and time delay can all accelerate the shift from the substantial state to the barren one of the ecological system, restrain the development of the vegetation system and weaken the stability of the ecological system. On the other hand, the additive noise strength always enhances the SNR and the SR phenomenon, while the intensity of multiplicative noise often reduces the effect of the SR. In particular, time delay can play different roles in exciting the SR phenomenon in different cases.     

Impact of time delay and a multiplicative periodic signal on stochastic resonance and steady states shift for a stochastic insect outbreak system subjected to Gaussian noises

In this paper, we aim to investigate comprehensively the steady-states characteristics, the stochastic resonance phenomenon and the mean decline time for an insect outbreak system caused by the terms of the multiplicative, additive noises and time delay,. Our results exhibit that the multiplicative noise and the time delay can both reduce the stability of the biological system and speed up the extinction process of the insect population, while the additive noise can decrease the possibility of the decline of the biological population by a wide margin and make contribution to the survival and reproduction of the insect system to some extent. On the other hand, as regards to the stochastic resonance phenomenon (SR) induced by noise terms, time delay term and a weak multiplicative periodic signal, the numerical results show that the multiplicative noise intensity Q always suppresses the SR effect in any case, while the additive noise intensity M can inhibit the SR effect in the case of a big value of Q, but excite the maximum of the SNR for the case of a small value of Q. Moreover, time delay τ exerts mainly the inhibitory effect on the SR phenomenon except that in the SNR-Q plot.     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Evidence of stochastic resonance in the mating behavior of Nezara viridula (L.)

We investigate the role of the noise in the mating behavior between individuals of Nezara viridula (L.), by analyzing the temporal and spectral features of the non-pulsed type female calling song emitted by single individuals.We have measured the threshold level for the signal detection, by performing experiments with the calling signal at different intensities and analyzing the insect response by directionality tests performed on a group of male individuals. By using a sub-threshold signal and an acoustic Gaussian noise source, we have investigated the insect response for different levels of noise, finding behavioral activation for suitable noise intensities. In particular, the percentage of insects which react to the sub-threshold signal, shows a non-monotonic behavior, characterized by the presence of a maximum, for increasing levels of the noise intensity. This constructive interplay between external noise and calling signal is the signature of the non-dynamical stochastic resonance phenomenon. Finally, we describe the behavioral activation statistics by a soft threshold model which shows stochastic resonance. We find that the maximum of the ensemble average of the input-output cross-correlation occurs at a value of the noise intensity very close to that for which the behavioral response has a maximum.