1,720,988 research outputs found
Field-induced stabilization of activation processes
No full textAn investigation of the noise activated escape from a metastable state and between attractors in a bistable system has been undertaken. It is demonstrated, both theoretically and by means of digital simulations, that the application of an external time-periodic field can lead to a significant increase in the lifetime (averaged over one period of the field) of a metastable state and in the residence time of a bistable system. In particular, it is shown that these characteristic times can be increased beyond the inverse Kramers rate calculated in the absence of the field. This effect is observed when the frequency of the external field is smaller than the unperturbed Kramers rate
Generic noise-enhanced coding in neuronal arrays
No full textWe demonstrate that, in a parallel array of model neurons, the optimizing influence of internal noise on the global information is far greater than that reported for a single neuron. In particular. stochastic resonance (SR) effects, that optimize information transmission, occur independent of stimulus level or the setting of the neural threshold. We further show that adjusting the threshold to maximize information transmission does not remove SR effects. Consequently, and in contrast to a single neuron, in neuronal arrays noise appears to be an essential element of an optimal coding strategy
ANALOG STOCHASTIC QUANTIZATION FOR A ONE-DIMENSIONAL BINARY ALLOY
No full textThe technique of analog stochastic quantization (ASQ), originally introduced in relation to the quantum harmonic oscillator, is applied to a more complicated quantum system: namely, a one-dimensional binary alloy. The results from an electronic analog simulator are compared with those obtained from numerical solutions of the Schrodinger equation, with which they are shown to be in agreement. It is argued on this basis that the ASQ technique can in principle be applied to one-dimensional quantum systems with arbitrary potentials
ZERO-FREQUENCY SPECTRAL PEAKS OF UNDERDAMPED NONLINEAR OSCILLATORS WITH ASYMMETRIC POTENTIALS
No full textThe spectral density of the fluctuations of an underdamped, single-well, nonlinear oscillator driven by a random force has been investigated. Electronic analog experiments have demonstrated the existence of a narrow spectral peak at zero frequency; such a peak only appears, however, in those cases where the potential is non-centro-symmetric. The evolution of the peak with variation of a parameter characterizing the asymmetry of the potential, and with noise intensity, has been investigated both experimentally and theoretically. It is found that the half-width of the peak remains relatively small (of the order of the reciprocal relaxation time) over a broad range of noise intensities. The theory of the peak shape is shown to be in close agreement with experiment. The relationships of the peak to the (apparently similar) zero-frequency peaks observed previously in double-well oscillators, where they are responsible for stochastic resonance, and to the supernarrow spectral peaks found near kinetic phase transitions in periodically driven systems, are discussed
Effect of external fluctuations on the Fréedericksz transition in an analogue simulator.
No full textThe influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Freedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemke et al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise
Influence of random fluctuations on delayed bifurcations : the case of additive white noise
Full text linkThe influence of additive white noise on the delay of a bifurcation point in the presence of a swept control parameter has been studied by analog experiment and digital simulation. Measurements of the time taken for the second moment [x^2(t)] to reach a given threshold are in excellent agreement with the calculations of Zeghlache, Mandel, and Van den Broeck [Phys, Rev. A 40, 286 (1989)). It is demonstrated, however, that the mean first-passage time (MFPT) for x^2(t) to attain the same threshold, corresponding to the quantity that is usually determined in laser experiments, can be markedly different. It may be either larger or smaller, depending on the conditions under which the measurements are made. A calculation of the MFPT is presented and shown to be in excellent agreement with the experimental measurements and to reduce, in the relevant limit, to the theoretical results previously published by Torrent and San Miguel [Phys. Rev. A 38, 245 (1988)]
Influence of random fluctuations on delayed bifurcations. II. The cases of white and colored additive and multiplicative noise
Full text linkThe influence of noise on the delay of a bifurcation point in the presence of a swept control parameter has been investigated theoretically, by digital simulation and by analog electronic experiment. The results obtained in an earlier paper [N. G. Stocks, R. Mannella, and P. V. E. McClintock, Phys. Rev. A 40, 5361 (989)] have thereby been extended and complemented. In particular, exact analytic expressions have been derived for the time-dependent probability densities P(x,t), and these have been used to obtain the mean first-passage time t*MFPT for x^2(t) to reach a threshold under the influence of Gaussian fluctuations, in several contexts: additive external white noise, additive external exponentially correlated noise, additive internal white noise, additive internal exponentially correlated noise, multiplicative white and colored noise. Based on Zeghlache, Mandel, and Van den Broeck's [Phys. Rev. A 40, 286 (989)] alternative definition of the bifurcation time t*moment in terms of the evolution of the second moment [x^2(t)], an expression is derived for t*moment for the general case of combined additive and multiplicative noises. The calculations are tested by comparison with the results of analog experiments and digital simulations, with which they are shown to be in excellent agreement
Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.
Full text linkStochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate
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