1,720,975 research outputs found
Generalized Wiener Process and Kolmogorov's Equation for Diffusion Induced by Non-Gaussian Noise Source
No full textWe show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the KolmogorovFeller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived
The problem of analytical calculation of barrier crossing characteristics for L ́evy flights
No full textBy using the backward fractional Fokker–Planck equation we
investigate the barrier crossing event in the presence of L ́evy noise. After
briefly reviewing recent results obtained with different approaches on the time
characteristics of the barrier crossing, we derive a general differential equation
useful to calculate the nonlinear relaxation time. We obtain analytically the
nonlinear relaxation time for free L ́evy flights and a closed expression in
quadrature of the same characteristics for the cubic potential
Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model
Full text linkThe phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics
densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant. In other words, at the output of the interneuron, inharmonious signals give rise to blurry spike trains, while the harmonious signals produce more regular, less noisy, spike trains. Theoretical results are compared
with numerical simulations
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
No full textNoise enhanced stability in fluctuating metastable states Phys. Rev. E69, 061103 (2004)
No full textWe derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain
the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise.We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a
function of the fluctuation rate of the potential
Diffusion Acceleration in Randomly Switching Sawtooth Potential
No full textWe investigate an overdamped Brownian motion in symmetric sawtooth periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ each other by a translation of half of period. The calculation of the effective diffusion coefficient is reduced to the mean first-passage time problem, and we obtain the exact expression valid for arbitrary mean rate of switchings and arbitrary intensity of white Gaussian noise. We find the area at parameters plane where acceleration of diffusion in comparison with the free diffusion case takes plac
Stability under influence of noise with regulated periodicity
No full textA very simple stochastic differential equation with quasi-periodical multiplicative noise is investigated analytically. For fixed noise intensity the system can be stable at high noise periodicity and unstable at low noise periodicity
Memristors and nonequilibrium stochastic multistable systems
No full textThe main aim of this special issue is to report the recent advances and new trends in memristors and nonequilibrium stochastic multistable systems, both theoretically and experimentally, within an interdisci-plinary context. In particular, memristors are multistable systems whose switching dynamics is a stochastic process, which can be controlled by internal and external noise sources, unveiling the constructive role of random fluctuations. Furthermore, the use of memristors as memory elements in neuromorphic systems with noise-assisted persistence of memory states, chaotic dynamics, metastable chaos and chaos synchronization, new stochastic nonlinear models, noise-induced phenomena such as stochastic resonance, noise enhanced stability and phase transitions phenomena in memristors will be illustrated in the contributions of this special issue
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