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Because noise is an inevitable attribute in gene regulatory networks, a stochastic differential equations model is constructed to study the impact of external noise on p53-Mdm2 regulatory network. Near the Hopf bifurcation of the corresponding deterministic model, external noise can induce stochastic resonance. When three stable steady states coexist in the corresponding deterministic model, external noise can lead to stochastic transition. Therefore, external noise can not only expand the parameter range of p53 regulatory network oscillations, but also increase the amplitude of p53 regulatory network oscillations, and is closely related to the outcome of cell fate. These findings deepen our understanding of the impact of external noise on gene regulatory networks and may provide new perspectives for the treatment of related diseases.

Synaptic plasticity is widely recognized to support adaptable information processing in the brain. Spike-timing-dependent plasticity, one subtype of plasticity, can lead to synchronous spike propagation with temporal spiking coding information. Recently, it was reported that in a noisy environment, like the actual brain, the spike-timing-dependent plasticity may be made efficient by the effect of stochastic resonance. In the stochastic resonance, the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal. However, previous studies have ignored the full variety of spiking patterns and many relevant factors in neural dynamics. Thus, in order to prove the physiological possibility for the enhancement of spike-timing-dependent plasticity by stochastic resonance, it is necessary to demonstrate that this stochastic resonance arises in realistic cortical neural systems. In this study, we evaluate this stochastic resonance phenomenon in the realistic cortical neural system described by the Izhikevich neuron model and compare the characteristics of typical spiking patterns of regular spiking, intrinsically bursting and chattering experimentally observed in the cortex.

We discuss stochastic resonance in associative memory with a canonical neural network model that describes the generic behavior of a large family of dynamical systems near bifurcation. Our result shows that stochastic resonance helps memory association. The relationship between stochastic resonance, associative memory, storage load, history of memory and initial states are studied. In intelligent systems like neural networks, it is likely that stochastic resonance combined with synaptic information enhances memory recalls.

In this work, we study the stochastic resonance phenomenon in a bistable nonlinear dynamical system in the presence of an uncorrelated noise source whose distribution decays asymptotically as P(ξ) ∝ 1/ξ^2α. We investigate the influence of the decay exponent α on the transition rate and on the optimal noise intensity giving the maximum signal-to-noise ratio when a weak periodic signal is superposed to the external noise. We find that the transition rate achieves a maximum for a finite decay exponent α. However, the optimal noise intensity for stochastic resonance depicts a monotonic power-law correction relative to the usual behavior of nonlinear dynamical systems driven by Gaussian noises.

Noise widely exists in the nervous system, and plays an extremely important role in the information processing of the nervous system, which can enhance or weaken the ability of the nervous system to process information. Nerve cells exist in complex and changeable electromagnetic fields, and their potential changes are significantly regulated by electromagnetic induction. In response to this, first, a memristor is used to simulate the electromagnetic field environment where the nervous system is located, when using different weak periodic signals as the input of the neuron system, the rich stochastic resonance behavior of the FitzHugh–Nagumo neuron system is analyzed under the drive of phase noise. Second, taking the amplitude, period and intensity of phase noise as the main change parameters, and the changes of the parameters of the memristor and the period of the external signal as auxiliary conditions, the stochastic resonance dynamics analysis is carried out from three perspectives: the amplitude and period of phase noise, the amplitude and intensity of phase noise and the intensity and period of phase noise.

Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on a Barabási–Albert network, subjected to weak periodic magnetic field. Spectral power amplification as a function of temperature shows strong dependence on the number of nodes, which is related to the dependence of the critical temperature for the ferromagnetic phase transition, and on the frequency of the periodic signal. Double maxima of the spectral power amplification evaluated from the time-dependent magnetization are observed for intermediate frequencies of the periodic signal, which are also dependent on the number of nodes. In the thermodynamic limit, the height of the maxima decreases to zero and stochastic resonance disappears. Results of numerical simulations are in qualitative agreement with predictions of the linear response theory in the mean-field approximation.

Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications — the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

We report a noise assisted and optimized resonant transition behavior between two metastable Turing pattern states in a piecewise FitzHu–Nagumo model. The response of the bistable Turing system to a weak periodic signal which modulates the attraction domain of the piecewise function is enhanced with the addition of noise. The quantity that measures the resonant transition between the bistable states and the periodicity of the Turing pattern shows a tent-shape dependence on the intensity of noise, which is the fingerprint of stochastic resonance. As the frequency of the signal is increased to be high enough, the coherent transition disappears.

The stochastic resonance phenomenon in a linear system subject to multiplicative and additive dichotomous noise is investigated. By the use of the linear-response theory and the properties of the dichotomous noise, the exact expressions have been found 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 additive dichotomous noise, and it varies non-monotonically with the bias of the external field, with the intensity and asymmetry of the multiplicative dichotomous noise, as well as with the external field frequency. Moreover, the SNR depends on the intensity of the cross noise between the multiplicative and additive dichotomous noise, as well as on the strength and asymmetry of the additive dichotomous noise.

We study stochastic resonance (SR) in Hindmarsh–Rose (HR) neural network with small-world (SW) connections driven by external periodic stimulus, focusing on the dependence of properties of SR on the network structure parameters. It is found that, the SW neural network enhances SR compared with single neuron. By turning coupling strength c, two categories of SR were gained. With the connection-rewiring probability p increasing, the resonance curve becomes more and more sharp and the peak value increases gradually and then reaches saturation. The SW network enhances the SR peak value compared with regular network and widens resonance in ascending range compared with random network. When decreasing node degree k, the resonance range is enlarged, and the signal noise ratio (SNR) curve becomes a two peak one from a classic single peak SR curve, and then the stochastic resonance phenomenon almost disappears.

Stochastic resonance in a chain of coupled threshold elements driven by a spatiotemporal periodic signal and noise is studied. It is shown that stochastic resonance can be enhanced for a fixed coupling strength by introducing proper time delays in the coupling terms which balance the effect of the phase difference between the periodic signals at the input of the interacting elements. Hence, in spatially extended systems driven by spatiotemporal periodic signals, stochastic resonance can be controlled by a delayed coupling. This method of controlling stochastic resonance is robust against random perturbations of the periodicity of the input signal and of the individual time delays.

Based on the single-mode laser noise model driven by quadratic colored pump noise and quantum noise with cross-correlation between real and imaginary parts of noise proposed in International Journal of Modern Physics B20, 5383 (2006) and Phys. Rev. E 73, 023802 (2006), the stochastic resonance (SR) of laser intensity is investigated by virtue of the linearized approximation. The analytic expression of signal-to-noise ratio (SNR) is calculated. It is found that the phenomena of stochastic resonance respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ_p and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency for the model. It is shown that there are three different types of SR in the model: the conventional form of SR, the SR in the broad sense and the bona fide SR.

We analyse time series of the Aerosol Index, a parameter related to the aerosol content and retrieved by satellite observations. In particular, we consider data recorded on oriental part of Sahara. A stochastic equation describes the behaviour of the Aerosol Index as occurs in Italy, but out of a stochastic resonance regime. We prove that, in the oriental part of Sahara, local dust source is simply linear superimposed to noise so that a stochastic resonance regime is not set. Furthermore, we find that the local dust emission strongly influences the Aerosol Index data and it is responsible for about 78% of the annual periodicity in the signal.

The phenomenon of stochastic resonance in a bistable system with multiple delays is investigated. The analytic expression of approximation stationary probability density is obtained by using small delay approximation based on probability density approach. Numerical simulation is performed and it is shown that the analytic results are in good agreement with Monte Carlo simulation. Then the expression of the signal-to-noise (SNR) is derived by using two-state theory. Finally, the effect of multiple delays on SNR is discussed. It is found that the stochastic resonance phenomenon can be suppressed or promoted when multiple delays are increased.

It is important to magnify natural stochastic resonance of nonlinear systems. In this paper, positive feedback is proposed to enhance stochastic resonance of those nonlinear systems whose internal parameters are difficult or impossible to be adjusted. The method can be used to improve the response of these nonlinear systems to external stimulus or strengthen the effect of target manipulation. At first, theoretical analysis based on adiabatic approximation method is presented, and then numerical simulations for both hard potential system and soft potential system are conducted to demonstrate the proposed method. Both theoretical analysis and numerical simulation indicate that stochastic resonance of these systems can be magnified by positive feedback.

In this work we analyze the transient dynamics of three different classical and quantum systems. First, we consider a classical Brownian particle moving in an asymmetric bistable potential, subject to a multiplicative and additive noise source. We investigate the role of these two noise sources on the life time of the metastable state. A nonmonotonic behavior of the lifetime as a function of both additive and multiplicative noise intensities is found, revealing the phenomenon of noise enhanced stability. Afterward, by using a Lotka–Volterra model, the dynamics of two competing species in the presence of Lévy noise sources is analyzed. Quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species are found. Finally the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir is investigated. We use the Caldeira–Leggett model and the approach of the Feynman–Vernon functional in discrete variable representation. We obtain the time evolution of the population distributions in energy eigenstates of the particle, for different values of the coupling strength with the thermal bath.

Asymmetric effects on the stochastic resonance (SR) in the bistable system with correlated noises are investigated. Based on the theory of signal-to-noise ratio (SNR), the expressions of SNR are derived for the case of the additive signal and the case of the multiplicative signal, respectively. Through the numerical computation, it is found in both cases of additive and multiplicative periodic signals (i) The asymmetric effects on SR phenomenon in the system induced by the multiplicative noise is dependent of initial conditions, i.e., the asymmetric parameter r weakens the SR for the initial condition of x(t = 0) = x₊, however, r enhances the SR for the initial condition of x(t = 0) = x_-; (ii) The asymmetric effects on SR phenomenon in the system induced by the additive noise and the correlation between noises is independent of initial conditions, i.e., the r always enhance the SR; (iii) Synergistic action of the noises, the correlation between noises, the periodic signal and the system's asymmetry induces symmetry revival.

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with colored coupling between multiplicative and additive noise terms is investigated. The SR can be induced by the multiplicative noise, the time delay and the coupling strength between noise terms. Meanwhile, the SR is affected by the initial condition of the system.

The output power and the signal-to-noise ratio (SNR) of a single-mode laser system are calculated in the case of the laser model with periodically modulated noise. The corresponding stochastic resonance (SR) phenomena are discussed and compared with the case without periodically modulated noise. It is shown that the main difference between the two noise laser models exists in the SNR as a function of signal period. There appears resonance and suppression coexisting phenomenon for the model with periodically modulated noise, which can be utilized to restrain or optimize the output SNR of the system. Whereas, SR is absent for the model without periodically modulated noise, and the SNR just increases monotonously with signal period.

The dynamics of charge carriers (electrons) hopping through a nonhomogeneous medium in semiconductor layer is investigated by changing a thermal noise of strength D and an external harmonic potential V(x). The nonhomogeneous medium exhibits denser trap distribution around the center, which biases the electrons to therein concentrate. Applying also a monostable potential at the center further enhances the accumulation of electrons. However, by applying a nonhomogeneous hot temperature in the vicinity of the potential minimum forced the electrons to diffuse away from the center and redistribute around two points. Thermally activated rate of hopping and diffusion of electrons in a nonhomogeneous medium, as a function of model parameters, is also considered in the high barrier limit. Using two states approximation, I have also studied the stochastic resonance (SR) of the electrons dynamics in the presence of a time-varying signal. I found a strong spectral amplification η and lower temperature occurrence of its peak as compared to previous works [M. Asfaw, B. Aragie and M. Bekele, Eur. Phys. J. B 79, 371 (2011); B. Aragie, Y. B. Tateka and M. Bekele, Eur. Phys. J. B 87, 101 (2014)].