Noise Enhanced Stability Phenomenon Research Articles

Correlated non-Gaussian and Gaussian noises induced transition and mean first-passage time in a fractional-order bistable system

The transition and mean first-passage time(MFPT) in a fractional-order bistable system, excited by multiplicative non-Gaussian noise and additive Gaussian white noise, are investigated. Utilizing the fractional-order minimum mean square error criterion and the path integral approach, we derive approximate expressions for both the steady-state probability distribution function and the MFPT. The results show that the noise correlation strength, non-Gaussian parameter, Gaussian noise strength and fractional order can induce phase transitions. The MFPT exhibits a peak as a function of non-Gaussian noise intensity, demonstrating the noise-enhanced stability phenomenon, while the MFPT displays a consistent, monotonic relationship as a function of Gaussian white noise intensity. Numerical simulations are conducted to validate theoretical results, which show a reasonably high degree of consistency.

Dynamic Properties for Time-Delayed Grazing Ecosystem Driven by Lévy Noise and Gaussian Noise

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.

Breather dynamics in a stochastic sine-Gordon equation: Evidence of noise-enhanced stability

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to illustrate the effectiveness of the noise-enhanced stability phenomenon, which manifests itself as a nonmonotonic behavior of the mean first-passage time for the breather as a function of the noise intensity. The influence of the mode’s initial frequency on the results and their robustness against an additional thermal background are also addressed. Overall, the analysis highlights a counter-intuitive, positive role of noise in the breather’s persistence.

Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries driven by multiplicative and additive noise

The performance of an unsaturated piecewise bistable stochastic resonance (UPBSR) with three kinds of asymmetries driven by multiplicative and additive Gaussian white noise is investigated. Firstly, by introducing an asymmetric factor into UPBSR potential, three kinds of asymmetries are constructed, i.e., well-depth asymmetry (WDA), well-width asymmetry (WWA), and both well-depth and well-width asymmetry (BDWA). Then, by deriving the output signal-to-noise ratio (SNR), the behavior of asymmetric UPBSR under two independent noises and correlated noises is analyzed. Enhancement ability and noise immunity are adopted as SR evaluation index. Moreover, the mean first passage time (MFPT), is adopted to discuss the transient properties of UPBSR system. Finally, for SNR analysis, the results show that asymmetric SR outperforms symmetric SR when the asymmetric factor is in the appropriate range, and the BDWA dominates the three cases. When subject to two independent noises, multiplicative noises always shows a suppression on SR. However, when the two noises are correlated, the effect of each parameter on SNR becomes complicated, the same parameter may have the exact opposite effect on SNR in different situations. In addition, the correlation intensity λ play an important role in SR. It can excite SR to appear as a double peak, which is different from the conventional SR. Despite the effects of individual parameters on SNR are highly coupled, the introduction of three kinds of asymmetries and correlated noise can improve the performance of SR. As for MFPT analysis, when driven by independent multiplicative and additive noise, MFPT exhibits similar monotonically decreasing behavior in various cases. However, the noise-enhanced stability (NES) phenomenon is excited when driven by the correlated multiplicative and additive noise. In the case of WDA and BDWA, both appropriate λ and noise intensity ratio R favor the NES phenomenon, while in the case of WWA, the NES phenomenon is suppressed.

The role of harvesting in population control in the presence of correlated noise sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of correlated noise sources. Our aim is to determine a statistical correlation between the noises in the model parameters and population size. The characteristic time scale over which the population size of prey and predator varies are very much different, this fact justifies to consider a single species model as the predator population can be chosen to be constant within the generation time of prey. Steady state probability distributions and stationary potentials of the population are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant harvesting. One of our key findings is the transition from bistable to tristable state for weak noises. Another valuable finding is the noise enhanced stability phenomenon for negatively correlated noises. Constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case to reduce population size. The obtained results may be helpful to understand toxin producing phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak or extinction in forest.

Effects of correlated noises on binocular rivalry

Visual pathways are inherently stochastic and thus noisy. Such fluctuation is generally considered to be a nuisance, actually, it shows potential benefits to perceptual alteration. Here, we investigated binocular rivalry subjected to correlated noises (correlation between additive noise and multiplicative noise). Our numerical results reveal that: (i) Noise enhanced stability phenomenon appears for the correlated case, while vanishes for the uncorrelated case; (ii) Multiplicative noise intensity presents very limited impact on the perceptual alternation under some certain additive noise intensities; (iii) Coherence resonance takes place for negative correlation, while disappears for positive or non correlation; (iv) Imbalance of perceptual dominance, caused by the correlation strengthen difference between the eyes, weakens the perceptual stability, but it has beneficial effects for inducement of coherence resonance. These findings have the significant implication for a deeper understanding of rivalry and its relationship to binocular vision.PACS numbers: 02.50.-r, 05.40.-a, 87.10.-e

Effect of internal noise on the relaxation time of an yttria stabilized zirconia-based memristor

The effects of temperature on the switching kinetics of an yttrium-stabilized zirconia-based memristor from a low-resistance state to a high-resistance state have been experimentally investigated. It was found that the memristor relaxation time depends on the temperature in a non-monotonous way, with a maximum observed at the temperature close to 55 °C. This nonmonotonic behavior is a signature of the noise-enhanced stability phenomenon observed in all physical and complex systems characterized by metastable states.

SNR gain enhancement in a generalized matched filter using artificial optimal noise

For a weak signal buried in a given background noisy environment, a generalized matched filter composed of nonlinearities and weight coefficients is investigated by exploring the potential benefit of the artificial noise. With the output signal-to-noise ratio (SNR) of the conventional linear matched filter as a benchmark, the SNR gain of the generalized matched filter is proven to be possibly improved by adding an optimal noise into the easily implemented nonlinearity. From the practical point of view, even if the filter itself has an adaptability to the noisy environment, the approach of adaptive stochastic resonance still finds an optimal non-zero amount of added noise to enhance the SNR gain of the generalized matched filter. Interestingly, the optimal added noise found by the adaptive stochastic resonance method can also maximize another meaningful measure of the mean residence time (MRT), which provides more physical insight to the generalized matched filter in the sense of the noise-enhanced stability phenomenon. These obtained results indicate an extended application of the incorporation of noise in the nonlinear filter design.

Impact of time delays and environmental noise on the extinction of a population dynamics model

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.Graphic abstract

Statistics of residence time for Lévy flights in unstable parabolic potentials.

We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.

The stability analysis of tumor-immune responses to chemotherapy system driven by Gaussian colored noises

Abstract The influence of Gaussian colored noises on the stability of tumor-immune responses to chemotherapy system is analyzed. By means of the unified colored noise approximation of multidimensional stochastic dynamic system, the system is changed into the stochastic system with Gaussian white noises. I derive the analytic formula of the maximum Lyapunov exponent of system as a function of intensities and correlation times of Gaussian colored noises, then I find the noise-enhanced stability phenomenon, which is detected by the maximum Lyapunov exponent. Moreover, the correlation time τ1 of ξ1(t) influences the stability of steady state becomes unstable if τ1 → 0.15, which also increases as the correlation time τ2 of ξ2(t) increases. These indicate that, once tumor grows, by controlling the stochastic effect in process of chemotherapy, such as Gaussian colored noises, it is possible to control the stability of the tumor, which is very important for treatment. Especially, one could regulate the correlation time τ1 for this purpose.

Estimating the nonlinear effects of an ecological system driven by Ornstein-Uhlenbeck noise

• An effective FPE for a dynamical system driven by multiple O-U noises is derived. • A Levins model driven by O-U noise and cross-correlated noise is constructed. • Noise enhanced stability phenomena is observed. In this paper, a simple ecological model driven by Ornstein-Uhlenbeck noise and cross-correlated noise is constructed based on the classical Levins model. Initially, an approximate Fokker-Planck Equation for a general dynamical system driven by multiple sources of Ornstein-Uhlenbeck and cross-correlated noise is obtained by using the unified colored-noise approximation method and the stochastic equivalent rules. Then, the effects of Ornstein-Uhlenbeck noise on the dynamical characteristics of the modified Levins model are investigated. The theoretical dynamical quantities, including the steady-state probability distribution function and the mean extinction time, respectively, are analyzed. It is found that the external noises can lead to a decrease in the probability of an occupied patch, while, the internal noise, the cross-correlated noise and the self-correlation time of the external and internal noises can cause an increase in the probability of an occupied patch. Further, the impact of the noise intensities on the mean extinction time is analyzed. It is especially worthy to note that as the intensities of the internal noise and the cross-correlated noise increase, a noise-enhanced stability phenomenon is induced. Moreover, the mean extinction time increases as the self-correlated time and the intensity of the cross-correlated noise increase, yet the mean extinction time decreases as the intensity of the internal noise increases. The validity of theoretical method is checked by numerical simulation.

Fluctuations-induced regime shifts in the Endogenous Credit system with time delay

Abstract The model of endogenous credit that exhibits multiple steady states and generates phase transitions with catastrophic abruptness has been investigated. This resembles aspects of financial meltdowns witnessed in global capital markets in 2007. In this paper, time delay and fluctuations (noises) are introduced into the endogenous credit model, and a stochastic asset price dynamics model with time delay is established. The effects of time delay, fluctuations and cross-correlation between two noises on the probability distribution and the mean first passage time (MFPT) are analyzed, and the theoretical results are in agreement with the numerical results. It is shown from time series and probability distribution that the noises and time delay can induce regime shifts between two stable states. For the positive cross-correlation between two noises (λ > 0.0), the MFPT exhibits a maximum for some characteristic values of the noise intensity, which identifies the signature of the noise-enhanced stability (NES) phenomenon for asset price. The cross-correlation between two noises enhances the NES phenomenon for asset price, while time delay weakens it. However for the zero and negative intensity of noise correlation (λ ≤ 0.0), the MFPT decreases as the noise intensity increases, namely, the NES phenomenon disappears for λ ≤ 0.0.

Nonequilibrium electron spin relaxation in n-type doped GaAs sample

Non-equilibrium electron spin relaxation in a n-type doped GaAs bulk semiconductor is investigated. We use a semiclassical Monte Carlo approach by considering multivalley spin dynamics of drifting electrons. Spin relaxation is considered through the D’yakonov–Perel mechanism, which is the dominant process in III–V semiconductors. An analytical expression for the inhomogeneous broadening of spin precession vector is derived by taking into account the effect of the electric field and the doping density. The inclusion of electron–electron scattering has the effect of increasing both the spin lifetime and the depolarization length. In particular, we find a non-monotonic trend with the maximum of both the spin lifetime and the depolarization length, as a function of the lattice temperature. This peculiar behavior, which is due to the nonlinear spin-lattice interaction through the phononic thermal bath, is akin to the noise-enhanced stability phenomenon. Moreover, for lattice temperatures up to 77 K the electron spin lifetime slightly increases with the doping density, while the spin depolarization length shows a decreasing behaviour. For electic field amplitudes higher than the threshold field (Gunn field), the spin lifetime increases with the lattice temperature. Our numerical findings are validated by a good agreement with the available experimental results.

Noise- and delay-enhanced stability in a nonlinear isolation system

In this paper, we present a detailed study of time-delayed feedback control of the nonlinear vibration isolation system driven by stochastic environmental fluctuations. We investigate the effects of time-delayed control force and nonlinear damping on the mean first passage time from the periodic attractors to reveal the complicated nonlinear stochastic dynamics of this system. Varying the intensities of noise sources, we find that the mean lifetime of the lower amplitude periodic attractor is characterized by nonmonotonic behavior as a function of the noise intensities. One remarkable behavior is the phenomenon of noise-enhanced stability has been carried out to evaluate the isolation performance of the controlled system. Moreover, the proper time delay value is obtained based on the consideration for the noise- and delay-enhanced stability. Finally, we observe that these transient properties are connected with the dynamics of time-delayed active control. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control isolation effectiveness, which provides the guidance for optimizing time-delayed active control for stochastic fluctuations in engineering practices.

Dynamics and energy generation of a hybrid energy harvester under colored noise excitations

A hybrid energy harvester combining piezoelectric and electromagnetic transduction mechanisms is presented, which can be extensively applied in harvest vibration energy. This paper studies power harvested from the hybrid harvester under additive and multiplicative Gaussian colored noise excitations. Based on the stochastic averaging method, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and reveal interesting dynamics related to the stationary probability density, mean harvested power and mean switching time. It is observed that noise intensities, correlation times and other system parameters will induce the appearance of stochastic bifurcation. Furthermore, the mean harvested power is carried out to understand the device output performance of the hybrid generators. The hybrid energy harvested can be enhanced by suitable choice of noise intensities, correlation times and other system parameters. Finally, the mean switching times of the periodic attractors are investigated. The phenomenon of noise-enhanced stability has been carried out to evaluate the performance of the hybrid energy harvester. The occurrence of the noise-induced stability phenomenon signifies that the stability of the large-amplitude periodic attractor can be enhanced by the noises, which is very beneficial for energy harvesting.

Dynamics of a stochastic system driven by cross-correlated sine-Wiener bounded noises

The sine-Wiener noise, as one new type of bounded noise and a natural tool to model fluctuations in dynamical systems, has been applied to problems in a variety of areas, especially in biomolecular networks and neural models. In this paper, by virtue of the Novikov theorem, Fox’s approach, and the ansatz of Hanggi, an approximate Fokker–Planck equation is derived for an one-dimensional Langevin-type equation with cross-correlated sine-Wiener noise. Meanwhile, the dynamical characters of a bistable system driven by cross-correlated sine-Wiener noise are investigated by applying the approximate theoretical method. For the bistable system, the cross-correlation intensity $$\lambda $$ can induce the reentrance-like phase transition, while the other noise intensities and the self-correlation time, except for the self-correlation time of additive bounded noise, can induce the first-order-like phase transition. The transition from the stable state to another one can be accelerated by $$\alpha $$ (additive bounded noise intensity), $$\tau _1$$ (the self-correlation time of the multiplicative bounded noise), and $$\tau _2$$ (the self-correlation time of the additive bounded noise) and can be restrained with $$\lambda $$ and $$\tau _3$$ (self-correlation time of the cross-correlation bounded noise). It is interesting that the noise-enhanced stability phenomenon is observed with D (multiplicative bounded noise intensity) varying for the positive correlation ($$\lambda >0$$) and is enhanced as $$\lambda $$ increases. The numerical results are in basic agreement with the theoretical predictions.

Stabilization by dissipation and stochastic resonant activation in quantum metastable systems

In this tutorial paper we present a comprehensive review of the escape dynamics from quantum metastable states in dissipative systems and related noise-induced effects. We analyze the role of dissipation and driving in the escape process from quantum metastable states with and without an external driving force, starting from a nonequilibrium initial condition. We use the Caldeira–Leggett model and a non-perturbative theoretical technique within the Feynman–Vernon influence functional approach in strong dissipation regime. In the absence of driving, we find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect in the quantum metastable system. In the presence of an external driving, the escape time from the metastable region has a nonmonotonic behavior as a function of the frequency of the driving, the thermal-bath coupling and the temperature. The quantum noise enhanced stability phenomenon is observed in both systems investigated. Finally, we analyze the resonantly activated escape from a quantum metastable state in the spin-boson model. We find quantum stochastic resonant activation, that is the presence of a minimum in the escape time as a function of the driving frequency. Background and introductory material has been added in the first three sections of the paper to make this tutorial review reasonably self-contained and readable for graduate students and non-specialists from related areas.

Harmonic velocity noise and its resonance in classical systems

We investigate a harmonic velocity noise and its resonance effect in classical linear and bistable systems. The harmonic velocity noise can be obtained via RLC oscillation circuit driven by the classical Gaussian white noise. Our numerical results indicate that mean square displacement of a free Brownian particle under action of the noise tends to be zero. In the classical systems, the noise not only suppresses fluctuation of particle but also induces resonance effect. Moreover, a noise-enhanced stability phenomenon in the bistable system is also found.

Lévy noise induced transition and enhanced stability in a gene regulatory network.

We investigate a quantitative bistable two-dimensional model (MeKS network) of gene expression dynamics describing the competence development in the Bacillus subtilis under the influence of Lévy as well as Brownian motions. To analyze the transitions between the vegetative and the competence regions therein, two dimensionless deterministic quantities, the mean first exit time (MFET) and the first escape probability, are determined from a microscopic perspective, as well as their averaged versions from a macroscopic perspective. The relative contribution factor λ, the ratio of non-Gaussian and Gaussian noise strengths, is adopted to identify an optimum choice in these transitions. Additionally, we use a recent geometric concept, the stochastic basin of attraction (SBA), to exhibit a pictorial comprehension about the influence of the Lévy motion on the basin stability of the competence state. Our main results indicate that (i) the transitions between the vegetative and the competence regions can be induced by the noise intensities, the relative contribution factor λ and the Lévy motion index α; (ii) a higher noise intensity and a larger α with smaller jump magnitude make the MFET shorter, and the MFET as a function of λ exhibits one maximum value, which is a signature of the noise-enhanced stability phenomenon for the vegetative state; (iii) a larger α makes the transition from the vegetative to the adjacent competence region to occur at the highest probability. The Lévy motion index α0≈0.5 (a larger jump magnitude with a lower frequency) is an ideal choice to implement the transition to the non-adjacent competence region; (iv) there is an expansion in SBA when α decreases.