Adaptive Bistable Stochastic Resonance Based Weak Signal Reception in Additive Laplacian Noise

Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance （ESR） in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio （SNR） is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance （SR） in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio （SNR） is calculated according to the generalized two-state theory （shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 （1999） 136]）. We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR.

The correlation between stochastic resonance and the average phase-synchronization time of a bistable system driven by colour-correlated noises

This paper investigates the correlation between stochastic resonance （SR） and the average phase-synchronization time which is between the input signal and the output signal in a bistable system driven by colour-correlated noises. The results show that the output signal-to-noise ratio can reach a maximum with the increase of the average phase- synchronization time, which may be helpful for understanding the principle of SR from the point of synchronization; however, SR and the maximum of the average phase-synchronization time appear at different optimal noise level, moreover, the effects on them of additive and multiplicative noise are different.

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance （SR） is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR： the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio （SNR） is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.

Stochastic Resonance of Instantaneous-State in Linear Regime of Single-Mode Lasers Driven by Colored Noises

According to a linear equation of the laser intensity of single-mode laser with input signal, we compute the generalized signal-to-noise ratio （GSNR） in the instantaneous-state of the single-mode laser, which is driven by two colored noises and correlated in the form of an e-exponential function. We detect that the stochastic resonance （SR） also occurs on instantaneous state at any time. Furthermore we discuss the GSNR trend to stable state in three different forms when taking different signal frequencies.

Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio （SNR）. It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.

Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise

This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise. Under the adiabatic approximation condition, the expression of the signal-to-noise ratio （SNR） is obtained. It finds that the SNR is a non-monotonic function of the delayed times, of the amplitude of the driving square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters. Moreover, the SNR depends non-monotonically on the correlate rate of the dichotomous noise.

Stochastic resonance in a time-delayed mono-stable system with correlated multiplicative and additive white noise

This paper considers the stochastic resonance for a time-delayed mono-stable system, driven by correlated multiplicative and additive white noise. It finds that the output signal-to-noise ratio （SNR） varies non-monotonically with the delayed times. The SNR varies non-monotonically with the increase of the intensities of the multiplicative and additive noise, with the increase of the correlation strength between the two noises, as well as with the system parameter.

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.

Experiment and application of parameter-induced stochastic resonance in an over-damped random linear system

This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.

Comparison of Signal to Noise Ratios by Stochastic Resonance Device and by Optimal Linear Filter

The signal to noise ratio (SNR) obtained by the devices for manifesting stochastic resonance (SR) can be larger than that by the optimal linear filter. The essential reason for this fact is that there is an energy transfer from noise to signal under the SR condition which is absent in the linear case.

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 exam- ined, and some mechanisms of the LEvy noise-induced SR are presented which are different from those of the Gaussian noise.

Parameter-induced stochastic resonance with a periodic signal

In this paper conventional stochastic resonance （CSR） is realized by adding the noise intensity. This demonstrates that tuning the system parameters with fixed noise can make the noise play a constructive role and realize parameter- induced stochastic resonance （PSR）. PSR can be interpreted as changing the intrinsic characteristic of the dynamical system to yield the cooperative effect between the stochastic-subjected nonlinear system and the external periodic force. This can be realized at any noise intensity, which greatly differs from CSR that is realized under the condition of the initial noise intensity not greater than the resonance level. Moreover, it is proved that PSR is different from the optimization of system parameters.

Implication of two-coupled tri-stable stochastic resonance in weak signal detection

Stochastic resonance （SR） has been proved to be an effective approach to extract weak signals overwhelmed in noise. However, the detection effect of current SR models is still unsatisfactory. Here, a coupled tri-stable stochastic resonance （CTSSR） model is proposed to further increase the output signal-to-noise ratio （SNR） and improve the detection effect of SR. The effects of parameters a, b, c, and r in the proposed resonance system on the SNR are studied, by which we determine a set of parameters that is relatively optimal to implement a comparison with other classical SR models. Numerical experiment results indicate that this proposed model performs better in weak signal detection applications than the classical ones with merits of higher output SNR and better anti-noise capability.

Harmonic stochastic resonance-enhanced signal detecting in NW small-world neural network

The harmonic stochastic resonance-enhanced signal detecting in Newman-Watts small-world neural network is studied using the Hodgkin-Huxley dynamical equation with noise. If the connection probability p, coupling strength gsyn and noise intensity D matches well, higher order resonance will be found and an optimal signal-to-noise ratio will be obtained. Then, the reasons are given to explain the mechanism of this appearance.

Local Correlated Noise Improvement of Signal-to-Noise Ratio Gain in an Ensemble of Noisy Neuron

We theoretically investigate the collective response of an ensemble of leaky integrate-and-fire neuron units to a noisy periodic signal by including local spatially correlated noise. By using the linear response theory, we obtained the analytic expression of signal-to-noise ratio (SNR). Numerical simulation results show that the rms amplitude of internal noise can be increased up to?an optimal value where the output SNR reaches a maximum value. Due to the existence of the local spatially correlated noise in the units of the ensemble, the SNR gain of the collective ensemble response can exceed unity and can be optimized when the nearest-neighborhood correlation is negative. This nonlinear collective phenomenon of SNR gain amplification in an ensemble of leaky integrate-and-fire neuron units can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and?amplitude of the weak periodic signal. The present study illustrates the potential to utilize the local spatially correlation noise and the number of ensemble units for optimizing the collective response of the neuron to inputs, as well as a guidance in the design of information processing devices to weak signal detection.

Stochastic resonance in surface catalytic oxidation of carbon monoxide induced by colored noise

The dynamical behavior of surface catalytic oxidation reaction of Pt(110)/CO+O2 modulated by colored noise, under the condition of specific temperature, has been investigated when the partial pressure of CO gas is near the supercritical Hopf bifurcation point. By computer simulation the oscillation and stochastic resonance induced by colored noise are observed. The influences of the intensity and correlation time of colored noise on stochastic resonance are discussed. The range of sensitivity of the system to the environmental fluctuation is analyzed.

Stochastic resonance in an optical bistable system subjected to cross-correlated additive white noise and multiplicative colored noise

The stochastic resonance （SR） of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio （SNR）. Results show that cross-correlation intensity λ enforces the SR of the system. The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ （τ is the self-correlation time of the multiplicative colored noise）. We find the SR phenomenon in the SNR-D and SNR-Q curves （D and Q are the intensities of the additive and multiplicative noises, respectively）, but not in the SNR-λ curves.

Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance （SR） in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio （SNR）. Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.