Noise-induced Stochastic Resonance Research Articles

Moment dynamics for stochastic resonance in active rotator systems

We investigate the dynamics of active rotator systems by the moment closure method based on matching derivatives. This method is illustrated and verified in terms of three systems: the single-element rotator, the two coupled rotators and the mean field coupled rotators. Using the moment closure method, we study the effect of common noise on active rotator systems from the perspective of stochastic resonance. It is shown that the noise-induced stochastic resonance and parameter-induced stochastic resonance occur in the above three systems. Our observation discloses that the two kinds of stochastic resonance effect can be enhanced by both increasing coupling strength and the number of coupled rotators.

Enhanced energy harvesting using time-delayed feedback control from random rotational environment

Motivated by improving performance of a bi-stable vibration energy harvester (VEH) from the viewpoint of vibration control, the time-delayed feedback control of displacement and velocity are constructively proposed into an electromechanical coupled VEH mounted on a rotational automobile tire, which is subject to colored noise and the periodic excitation. Using the improved stochastic averaging procedure based on energy-dependent frequency, the expressions of stationary probability density (SPD) and signal-to-noise ratio (SNR) are obtained analytically. Then, the efficiency of time-delayed feedback control on the stationary response and stochastic resonance (SR) for the delay-controlled VEH is explored in detail theoretically. Results show that both noise-induced SR and delay-induced SR can occur. Time delay is able to not only enhance the SR behavior but also weaken it. Furthermore, a larger negative feedback gain of displacement and a larger positive feedback gain of velocity are more beneficial for VEH. Interesting finding is that the optimal combination of time delay in maximizing the harvested performance, such as the harvest power, the output voltage and the power conversion efficiency, is almost perfectly consistent with that in maximizing SNR. Compared with the uncontrolled VEH, the delay-controlled VEH can achieve certain desirable optimization in harvesting energy by choosing the appropriate combination of time delays and feedback gains.

Stochastic resonance of a tri-stable system with α stable noise

A tri-stable system excited by weak periodic signal is taken as a model and the stochastic resonance phenomenon is investigated by additive α stable noise in this paper. The laws for the resonance system parameters q, p, skewness parameter r and intensity amplification factor Q of α stable noise to act on the resonant output are explored under different stability indicies α and asymmetric skewness β of α stable noise. The results indicate that a weak signal can be realized by tuning the system parameters q, p and r under the joint action of additive α stable noise, and the interval of q and p which can induce stochastic resonance does not change with α or β. Moreover, a certain rule is found in which adjusting the intensity amplification factor Q of α stable noise can also realize a synergistic effect when studying the noise-induced stochastic resonance, and the interval of Q does not change with α or β; the best value of the characteristic index is α=1 under any system parameter, and the best value of the symmetry parameter is β=1 under any system parameter. So, the system performance is best when α=1 and β=1. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.

Effects of hybrid synapses and partial time delay on stochastic resonance in a small-world neuronal network

In real neuronal systems, information transition delay is an inevitable factor. However, between some neurons, neuronal information is transmitted instantaneously or the time delay is too small and can be neglected. Thus, differing from the conventional studies where all connections are considered to be delayed, here we mainly focus on the effect of partial time delay on stochastic resonance in a Watts-Strogatz small-world neuronal network. Meanwhile, in the same neuronal network, the electrical and chemical synapses usually coexist. Thus, effects of hybrid synapses are also considered. Firstly, in the absence of time delay, noise could induce stochastic resonance when the neuronal network contains much more excitatory synapses than inhibitory ones; while it cannot induce stochastic resonance vise verse. Interestingly, it is further revealed that when the ratio of excitatory synapse to inhibitory synapse is approximately 4:1, noise-induced stochastic resonance is more robust. Thus, to discuss the effects of other factors on noise-induced stochastic resonance, we set this ratio to be 4:1. In the absence of time delay, we also consider effects of chemical synapses with a ratio of excitatory synapse to inhibitory synapse of 4:1 on the noise-induced stochastic resonance. The obtained results show that the noise could always induce stochastic resonance no matter how the probability of chemical synapses varies. And the optimal noise intensity increases linearly with the probability of chemical synapses increasing. For partial time delay, it is surprisingly found that the stochastic resonance could appear multiple times with the variation of the time delay being just for small partial time delay probability. Moreover, chemical synapse is found to facilitate this effect of partial time delay. Finally, by analyzing the joint effects of partial time delay and noise intensity, it is found that the larger the time delay and the partial time delay probability are, the wider the optimal noise region corresponding to large response amplitude is.

Lévy noise induced stochastic resonance in an FHN model

This paper aims to investigate the stochastic resonance (SR) in an FitzHugh-Nagumo (FHN) model with an additive Levy noise numerically. The non-Gaussian Levy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio (SNR), and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the Levy noise and the FHN model on the SR will be examined, and some mechanisms of the Levy noise-induced SR are presented which are different from those of the Gaussian noise.

Stochastic resonance of asymmetric bistable system with α stable noise

In this paper we take the asymmetric bistable system excited by weak periodic signal as a model and regard signal-to-noise ratio gain as an index to investigate the stochastic resonance phenomenon stimulated by additive and multiplicative α stable noise. Stochastic resonance phenomenon stimulated by only additive α stable noise is also investigated here. The laws for the resonance system parameters a, b, asymmetric skewness r and intensity amplification factor Q or D of α stable noise to act on the resonant output are explored under different stability index α and skewness parameter β of α stable noise. The results show that no matter whether under the joint action of additive and multiplicative α stable noise or under the action of only additive α stable noise, weak signal detection can be realized by tuning the system parameters a, b and r. The intervals of a, b and r which can induce stochastic resonances are multiple, and do not change with α nor β. Moreover, when investigating the noise-induced stochastic resonance, it is found that stochastic resonance can also be realized by tuning the intensity amplification factor of α stable noise. And the interval of D does not change with α nor β. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.

Characteristic analysis of power function type monostable stochastic resonance with Levy noise

In this paper, the Levy noise is combined with a power function type monostable stochastic resonance system for the first time. In order to ensure the reliability of the experimental data, the average signal-to-noise ratio gain is regarded as an index to investigate the stochastic resonance phenomenon stimulated by Levy noise. Potential function form of the monostable system and the method of generating Levy noise are presented in detail. The pulse characteristic and smear characteristic of Levy noise are also presented in detail. The laws for the resonant output of monostable system, governed by parameters a and b, the intensity amplification factor D of Levy noise, are explored under different values of characteristic index and symmetry parameter of Levy noise. Results show that no matter whether it is under any different characteristic index or symmetry parameter of Levy noise, the weak signal can be detected by adjusting the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with nor . Moreover, the same rule is founded which by adjusting the intensity amplification factor D of Levy noise can also realize synergistic effect when studying the noise-induced stochastic resonance, and the interval of D does not change with nor ; the best value of characteristic index is =1 under any system parameter, and the best value of symmetry parameter is =1 under any system parameter. So, the system performance is best when =1 and =1. Finally, the interaction relationship between system parameters a and b is investigated, and it is found that the interval of a or b will change with b or a when characteristic index , symmetry parameter and the intensity amplification factor D of Levy noise are fixed. These results will contribute to reasonably choosing the system parameters and intensity amplification factor of power function type monostable stochastic resonance system under Levy noise, and provide a reliable basis for practical engineering application of weak signal detection by stochastic resonance.

Dynamic response and stochastic resonance of a tri-stable system

Stochastic resonance (SR) describes a nonlinear phenomenon in nature, of which the essential ingredients are a nonlinear system, a weak signal, and a source of noise. Using the nonlinear system, the signal-to-noise ratio (SNR) of the output signal of the system will peak at a certain value of noise intensity under a synergistic action of input signal and noise. Besides the traditional Langevin equation, the new SR models such as monostable oscillators, chaotic systems, time-delay systems and bistable Duffing systems, can also produce SR phenomena. In this paper, a normalized symmetrical tri-stable potential function is constructed by using equilibrium parameters p and q, and a tri-stable system model simultaneously driven by weak signal and noise is further proposed. The tri-stable system model can be understood through a cantilever beam structure with three magnets, and deduced from the Brownian motion equation. We study in-depth and summarize the influences of parameters p and q on the potential barrier heights ΔU1, ΔU2 and their difference value. By analyzing the steady-state solution of the tri-stable system under invariable input, the concept of system steady-state solution curve (SSS curve) is proposed, and is used to further study the system dynamic response under low-frequency harmonic signal input. In these situations, the system response can be obtained by combining the steady-state solutions of the system following time t under a group of tempolabile inputs. Moreover, with the noise injection, the tri-stable system can realize SR under appropriate parameter condition, which can be demonstrated by the output amplitude curve and also the output SNR curve of the system against noise intensity. The mechanism of noise-induced SR of tri-stable system can be analyzed from the perspective of SSS curve. Finally, we further study the influence of tri-stable SR against system parameters. The value of damping ratio k affects the value of damping force acting on the Brownian particle, thus the tri-stable system needs noise with larger intensity to produce SR under a larger k. The values of equilibrium parameters p and q both affect the shape of the SSS curve, a larger p or a smaller q may result in larger-intensity noise for the system to produce SR.

Pinning noise-induced stochastic resonance

This paper proposes the concept of pinning noise and then investigates the phenomenon of stochastic resonance of coupled complex systems driven by pinning noise, where the noise has an α-stable distribution. Two kinds of pinning noise are taken into account: partial noise and switching noise. In particular, we establish a connection between switching noise and global noise when Gaussian noise is considered. It is shown that switching noise can not only achieve a stronger resonance effect, but it is also more robust to induce the resonance effect than partial noise.

Lévy noise-induced stochastic resonance in a bistable system

Stochastic resonance phenomenon induced by non-Gaussian L\'evy noise in a second-order bistable system is investigated. The signal-noise-ratio for different parameters is computed by an efficient numerical scheme. The influences of the noise intensity, stability index of L\'evy noise and amplitude of external signal on the occurrence of stochastic resonance phenomenon are characterized. This implies that a high amplitude of signal not only enhances the output power spectrum of system but also promotes stochastic resonance, and a proper adjustment of L\'evy noise intensity in a certain range enlarges the peak value of output power spectrum which is significant for stochastic resonance. Moreover, with the optimal damping parameter, lowering the stability index leads to larger fluctuations of L\'evy noise, and further reduces the chance of the stochastic resonance.

Stochastic Resonance in an Autoactivating Positive-Feedback Loop with Periodically Modulated Noise

Periodically modulated noise-induced stochastic resonance in an autoactivating positive-feedback loop with bistability is investigated, where the gene expression is assumed to be disturbed by both additive and multiplicative external noises. The signal-to-noise ratio (SNR) is calculated when the noise and the weak periodic force are introduced multiplicatively (rather then additively). The effects of the intensity α of additive noise and the intensities D1 and D2 of two types of multiplicative noises on the SNR are discussed. We compare the multiplicative introduction with the additive introduction between the noise and a weak periodic force. Research results show that (i) the maximum transcription rate kmax can produce a critical behavior in the SNR as a function of the noise intensity α, i.e., there is a critical value of kmax, below which the multiplicative introduction can enhance the maximum in the SNR, while above it is weakened; (ii) the additive introduction can enhance the maximum in the SNR as a function of the noise intensity D1; and (iii) the SNR as a function of the noise intensity D2 exhibits two maxima, i.e., the two maxima in the SNR identifies the characteristic of the double stochastic resonance, and the multiplicative introduction can enhance it.

Effects of multiscale noise tuning on stochastic resonance for weak signal detection

Noise enhanced signal detection via stochastic resonance (SR) is generally realized by white noise tuning with an optimal noise intensity. This paper explores a new mechanism of SR that is induced by the noise at multiple scales for enhanced detection of weak signals under heavy background noise. A strategy is proposed to realize the SR via multiscale noise tuning according to the property of 1/f noise. The presented new method combines the benefits of colored noise and parameter tuning to the SR phenomenon. Under the strategy, effects of noise intensity, analysis scale, and driving frequency on the SR are analyzed through numerical simulations. Three merits are displayed for the proposed multiscale noise-induced SR model: insensitivity to noise intensity, activity of multiple scale noise, and capability of detecting high frequency. A practical application to structural defect identification has confirmed the effectiveness of the proposed method in comparison with traditional methods.

Evaluation of an Asymmetric Bistable System for Signal Detection under Lévy Stable Noise

We evaluate the performance of a typical asymmetric bistable system for detecting aperiodic signal under Lévy stable noise. A Grünwald—Letnikov implicit finite difference method is employed to solve the fractional Fokker—Planck equation numerically. The noise-induced stochastic resonance (SR) and the parameter-induced SR both exist in the asymmetric bistable systems. The increase of the skewness parameter γ may deteriorate the system performance. However, by tuning the system parameters, the effects of asymmetry on the system performance can be reduced.

Application of Generalized Stochastic Resonance to the Vibration Test

Noise, bistable system and input signal are the three essential factors in stochastic resonance (SR). The noise-induced SR method, the parameter-tuning SR method, and the twice sampling SR method change the characteristics of the noise, the bistable system and the input signal, respectively. With the new cooperation, they can all produce the SR phenomena when the system exceeds the small-parameter area. If treating the strong noise and the input signal with large frequency, the actions of the system parameters can build the system behavior in an orderly way, associated with the twice sampling frequency. The united parameter-tuning SR method adjusts the system parameters to fit the normalized frequency after the twice sampling SR, in order to make the optimal noise intensity. The application to the flow meter vibration test has presented the practicability and effectiveness of the united parameter-tuning SR method.

A Demonstration of Equivalence between Parameter-Induced and Noise-Induced Stochastic Resonances with Multiplicative and Additive Noises

A typical bistable nonlinear system with multiplicative and additive noises can produce stochastic resonance (SR) by increasing the intensity of the additive noise or the multiplicative noise and it has been proved that SR can also be realized by tuning system parameters. We clearly demonstrate the equivalence between parameter-induced SR (PSR) and noise-induced SR in the presence of multiplicative and additive noises. By tuning several system parameters with fixed noise intensities, the SR is induced just as it is realized by tuning the additive noise or the multiplicative noise. It may be interesting to realize PSR when the noise intensity exceeds the resonance level, or when the characteristic of the noise is unknown.

Research on Virtual-Switch Characteristics of Noise-Enhanced Stochastic Resonance Using Leaky Integrate-and-Fire Model

Virtual-switch characteristics of noise-induced stochastic resonance using leaky integrate-and-fire (LIF) model was focused in this article. For LIF neuron model, Gaussian white noise was added to the simulating system. The condition of spike-starting was studied through the system. With the increase of noise intensity, the stimulated spikes became more and more intensive. With proper white noise intensity, the amount of excitatory spikes was enough to generate spike trains. We expected to design a virtual-switch utilizing this mechanism for neural data processing field.