Thermally enhanced stability in fluctuating bistable potentials

Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model

The behavior of a stochastic resonate-and-fire neuron model based on a reduction of a fractional noise-driven generalized Langevin equation (GLE) with a power-law memory kernel is considered. The effect of temporally correlated random activity of synaptic inputs, which arise from other neurons forming local and distant networks, is modeled as an additive fractional Gaussian noise in the GLE. Using a first-passage-time formulation, in certain system parameter domains exact expressions for the output interspike interval (ISI) density and for the survival probability (the probability that a spike is not generated) are derived and their dependence on input parameters, especially on the memory exponent, is analyzed. In the case of external white noise, it is shown that at intermediate values of the memory exponent the survival probability is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonancelike suppression of the probability of spike generation as a function of the memory exponent. Moreover, an examination of the dependence of multimodality in the ISI distribution on input parameters shows that there exists a critical memory exponent α_{c}≈0.402, which marks a dynamical transition in the behavior of the system. That phenomenon is illustrated by a phase diagram describing the emergence of three qualitatively different structures of the ISI distribution. Similarities and differences between the behavior of the model at internal and external noises are also discussed.

Statistics of a leaky integrate-and-fire model of neurons driven by dichotomous noise

The behavior of a stochastic leaky integrate-and-fire model of neurons is considered. The effect of temporally correlated random neuronal input is modeled as a colored two-level (dichotomous) Markovian noise. Relying on the Riemann method, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived, and their dependence on noise parameters (such as correlation time and amplitude) is analyzed. Particularly, noise-induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established. The features of spike statistics, analytically revealed in our study, are compared with recently obtained results for a perfect integrate-and-fire neuron model.

Memory effects for a trapped Brownian particle in viscoelastic shear flows

The long-time limit behavior of the positional distribution for an underdamped Brownian particle in a fluctuating harmonic potential well, which is simultaneously exposed to an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law-type memory kernel. The influence of a fluctuating environment is modeled by a multiplicative white noise (fluctuations of the stiffness of the trapping potential) and by an additive internal fractional Gaussian noise. The exact expressions of the second-order moments of the fluctuating position for the Brownian particle in the shear plane have been calculated. Also, shear-induced cross correlation between particle fluctuations along orthogonal directions as well as the angular momentum are found. It is shown that interplay of shear flow, memory, and multiplicative noise can generate a variety of cooperation effects, such as energetic instability, multiresonance versus the shear frequency, and memory-induced anomalous diffusion in the direction of the shear flow. Particularly, two different critical memory exponents have been found, which mark dynamical transitions from a stationary regime to a subdiffusive (or superdiffusive) regime of the system. Similarities and differences between the behaviors of the models with oscillatory and nonoscillatory shear flow are also discussed.

Generalized Langevin equation with multiplicative noise: temporal behavior of the autocorrelation functions

The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.

Thermal-inertial ratchet effects: negative mobility, resonant activation, noise-enhanced stability, and noise-weakened stability

Transport properties of a Brownian particle in thermal-inertial ratchets subject to an external time-oscillatory drive and a constant bias force are investigated. Since the phenomena of negative mobility, resonant activation and noise-enhance stability were reported before, in the present paper, we report some additional aspects of negative mobility, resonant activation and noise-enhance stability, such as the ingredients for the appearances of these phenomena, multiple resonant activation peaks, current reversals, noise-weakened stability, and so on.

Noise-induced enhancement of stability in a metastable system with damping

The mean first passage time of a Brownian particle from an initial unstable state in a metastable system with damping is investigated. The system is analyzed in the low to high damping regime, and the role played by the damping parameter is studied. We observe the noise enhanced stability effect for all the initial unstable states under study and for all values of the damping parameter γ investigated. The curves show a behavior of the mean first passage time vs γ very close to that observed for an overdamped particle in the presence of colored noise as a function of the correlation time.

Memory-enhanced energetic stability for a fractional oscillator with fluctuating frequency

The long-time limit behavior of the variance and the correlation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic-type friction kernel with memory is assumed as a power-law function of time. The exact expressions of stochastic resonance (SR) characteristics such as variance and signal-to-noise ratio (SNR) have been calculated. It is shown that at intermediate values of the memory exponent the energetic stability of the oscillator is significantly enhanced in comparison with the cases of strong and low memory. A multiresonancelike behavior of the variance and SNR as functions of the memory exponent is observed and a connection between this effect and the memory-induced enhancement of energetic stability is established. The effect of memory-induced energetic stability encountered in case the harmonic potential is absent, is also discussed.

Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions

In this paper, we investigate the net voltage in the Josephson junction subject to a thermal noise, a dc constant bias electric current and an ac time-periodic electric drive for the overdamped case and underdamped case simultaneously. It is shown that, by increasing the thermal noise strength, the net voltage can be decreased and increased several times as a function of the driving frequency. In addition, noise-enhanced stability is found for the net voltage of the junction.

Resonant behavior of a fractional oscillator with fluctuating frequency

The long-time behavior of the first moment for the output signal of a fractional oscillator with fluctuating frequency subjected to an external periodic force is considered. Colored fluctuations of the oscillator eigenfrequency are modeled as a dichotomous noise. The viscoelastic type friction kernel with memory is assumed as a power-law function of time. Using the Shapiro-Loginov formula, exact expressions for the response to an external periodic field and for the complex susceptibility are presented. On the basis of the exact formulas it is demonstrated that interplay of colored noise and memory can generate a variety of cooperation effects, such as multiresonances versus the driving frequency and the friction coefficient as well as stochastic resonance versus noise parameters. The necessary and sufficient conditions for the cooperation effects are also discussed. Particularly, two different critical memory exponents have been found, which mark dynamical transitions in the behavior of the system.