Noise-induced coupling and phase transition in initially homogeneous bistable system

We show that a colored spatial noise induces a heterogeneous behavior and coupling of initially uncoupled single bistable units. A formal approximation reduces a non-Markovian stochastic process described by the initial set of equations into Markovian process in terms of Langevin equation, for which a simple piecewise linear emulation was used to represent the nonlinear deterministic force. It turned out that the coupling leads to a phase transition due to the noise-induced diffusive term. As an example, a typical bistable noisy system with symmetric double-well potential was studied.     

Modulated noisy biological dynamics: Three examples

Three examples of noisy biological dynamics modulated by a periodic signal are discussed. A minimal neuron model driven by stochastic noise and small periodic force show a firing statistic comparable with stochastic resonance as demonstrated in bistable systems. Similar results are obtained from responses to periodic vibrotactile stimulation on higher-order neuronal units of the somatosensory pathway. Finally, results from a bistable visual perception task exhibiting stochastic resonance are reported.     

Frequency and phase synchronization in stochastic systems

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.     

随机共振控制的频率匹配方法

根据非线性双稳系统在噪声和弱周期信号作用下产生随机共振的随机同步条件，提出了随机共振控制的频率匹配方法.理论分析和数值仿真结果表明，随机共振是可控制的，通过控制输入信号的频率和噪声的统计特性，不仅能拓宽产生随机共振的频率范围，而且能增强共振的强度，从而实现有更多的噪声能量转换为信号能量. 关键词： 随机共振 非线性双稳系统 频率匹配 控制     

耦合双稳系统的随机共振控制

两个双稳系统经非线性耦合而成为多稳态系统,该耦合系统与单一双稳系统相比具有较高的理论研究和实际应用价值.解析地分析了耦合系统在含噪弱周期信号作用下的响应特性,给出了耦合系数和双稳系统参数对随机共振的影响,表明耦合系统的随机共振是在带状的双势阱作用下产生的,还构建了反馈耦合控制原理框图.这为在双稳类系统中人为地产生随机共振或使共振效应更加强烈即随机共振的控制及其应用提供了可靠的理论依据.数值仿真结果与理论分析完全符合. 关键词： 耦合双稳系统 随机共振 控制     

Synchronization of noise-induced bursts in noncoupled sensory neurons

We report experimental observation of phase synchronization in an array of nonidentical noncoupled noisy neuronal oscillators, due to stimulation with external noise. The synchronization derives from a noise-induced qualitative change in the firing pattern of single neurons, which changes from a quasiperiodic to a bursting mode. We show that at a certain noise intensity the onsets of bursts in different neurons become synchronized, even though the number of spikes inside the bursts may vary for different neurons. We demonstrate this effect both experimentally for the electroreceptor afferents of paddlefish, and numerically for a canonical phase model, and characterize it in terms of stochastic synchronization.     

System size stochastic resonance in driven finite arrays of coupled bistable elements

The global response to weak time periodic forces of an array of noisy, coupled nonlinear systems might show a nonmonotonic dependence on the number of units in the array. This effect has been termed system size stochastic resonance by other authors. In this paper, we focus on a collective variable of a finite array of one-dimensional globally coupled bistable elements. We analyze the possible nonmonotonic dependence on the system size of its power spectral amplification and its signal-to-noise ratio.     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

Coherence and stochastic resonance in a birhythmic van der Pol system

We consider the response to uncorrelated noise and harmonic excitation of a birhythmic van der Pol-type oscillator. This system, as opposed to the standard van der Pol oscillator, is characterized by two stable orbits. The noisy oscillator can be analytically mapped, with the technique of stochastic averaging, onto an ordinary bistable system with a bistable (quasi)potential. The birhythmic oscillator can also be numerically characterized through the diagnostics of coherent resonance and the signal-to-noise-ratio. The analysis shows the presence of noise-induced coherent states, influenced by the different time scales of the oscillator.     

The Availability of Logical Operation Induced by Dichotomous Noise for a Nonlinear Bistable System

Instead of a continuous system driven by Gaussian white noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon different from Gaussian white noise. We can realize two parallel logical operations by simply adjusting the values of these two thresholds. Besides, to quantify the reliability of obtaining the correct logic output, we numerically calculate the success probability, and effects of dichotomous noise on the success probability are observed, these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise.     

Stochastic resonance in underdamped,bistable systems

We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the nonperturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behaviour and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime.     

Stochastic resonance characteristic analysis of new potential function under Levy noise and bearing fault detection

Based on the output saturation of classcial bistable stochastic resonance (CBSR), a new type of piecewise nonlinear bistable stochastic resonance (PNBSR) system is constructed. The mean signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b and D of Levy noise are explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of PNBSR system has increased 4?dB by comparing with the output signal-to-noise ratio of CBSR system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise. The interval of the parameters of system which induces good stochastic resonance is roughly the same. And the output signal waveform of resonance is very similar to the input signal waveform, which has some reference value for the signal recovery. Moreover, we can find the good stochastic resonance interval of the system parameters do not change with D of Levy noise under the different noise intensity D of Levy noise. On the basis of this, adjusting the intensity amplification factor D of Levy noise, which induces good stochastic resonance, and the interval does not change with α or β. At last, the piecewise nonlinear bistable system is applied to detect bearing fault signals, which achieves better performance compared with the classical bistable system.     

Hopping and phase shifts in noisy periodically driven bistable systems

We consider a periodically driven bistable system in the presence of fluctuations. In a number of recent papers it has been shown that the amplitude of the response of the noisy system to periodic modulations exhibits stochastic resonance, i.e. a resonance-like behavior as a function of the noise intensity. In this paper, we consider the phase shift between the response and the periodic driving. For weak periodic driving, the phase shift also shows a resonance like behaviour as a function of the noise strength, but this effect is shown to be of different origin than the one responsible for stochastic resonance. Furthermore, the phase shift is demonstrated to exhibit a resonance-like behavior as a function of the driving frequency.     

Effect of multiplicative noise on parametric instabilities

We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.     

Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation

We analyze noise-induced phenomena in nonlinear dynamical systems near a subcritical Hopf bifurcation. We investigate qualitative changes of probability distributions (stochastic bifurcations), coherence resonance, and stochastic synchronization. These effects are studied in dynamical systems for which a subcritical Hopf bifurcation occurs. We perform analytical calculations, numerical simulations and experiments on an electronic circuit. For the generalized Van der Pol model we uncover the similarities between the behavior of a self-sustained oscillator characterized by a subcritical Hopf bifurcation and an excitable system. The analogy is manifested through coherence resonance and stochastic synchronization. In particular, we show both experimentally and numerically that stochastic oscillations that appear due to noise in a system with hard excitation, can be partially synchronized even outside the oscillatory regime of the deterministic system.     

Observation of stochastic resonance near a subcritical bifurcation

A hysteretic Subcritical period-doubling bifurcation is observed in the nonlinear strain dynamics of a magnetostrictive oscillator. The dynamic strain response of the magnetostrictive oscillator was observed with a high-resolution fiber optic interferometer. The effects of low-frequency modulation and band-limited stochastic fluctuations on such a bifurcation are investigated. Power spectral density measurements show that for an optimal value of externally injected noise the signal-to-noise ratio of a low-frequency modulation signal is enhanced by greater than 14 dB, thus indicating the first experimental observation of stochastic resonance near a bistable period-doubling bifurcation.     

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.     

Signal detection for frequency-shift keying via short-time stochastic resonance

A series of short-time stochastic resonance (SR) phenomena, realized in a bistable receiver, can be utilized to detect a train of information represented by signals that adopt frequency-shift keying (FSK). It is demonstrated that the values of noise intensity at resonance regions are close for adjacent periodic signals with an appropriate frequency separation. This establishes the possibility of decoding subthreshold or slightly suprathreshold M-ary FSK signals in bistable receivers. Furthermore, the mechanism of FSK signal detection via short-time SR effects is elucidated in terms of the receiver response speed. This phenomenon provides a possible mechanism for information processing in a bistable device operating in nonstationary noisy environments, where even the inputs appear over a short timescale or have a frequency shift.