Monostable array-enhanced stochastic resonance (original) (raw)
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Comment on “Monostable array-enhanced stochastic resonance”
Physical Review E, 2002
Lindner et al. ͓Phys. Rev. E 63, 051107 ͑2001͔͒ have reported multiple stochastic resonances ͑SRs͒ in an array of underdamped monostable nonlinear oscillators. This is in contrast to the single SR observed earlier in a similar but isolated oscillator. Though the idea that such an effect might occur is intuitively reasonable, the notation and the interpretation of some of the major results seem confusing. These issues are identified and some of them are clarified. In addition, comments are made on two possible extensions of the central idea of Lindner et al.: one of these promises to provide much more striking manifestations of multiple SR in arrays; the other significantly widens the range of systems in which multiple SRs may be observed.
Stochastic resonance in a parallel array of nonlinear dynamical elements
Physics Letters A, 2008
In an uncoupled parallel array of bistable dynamical elements subject to a common noisy subthreshold rectangular signal, the signal-to-noise ratio (SNR) gain can be improved by tuning the internally added array noise. A SNR gain above unity is observed in certain regions of the array noise intensity. The maximum SNR gain is obtained as the size of the array goes to infinity. This form of stochastic resonance (SR), i.e., array SR, is analytically described by introducing a quasi-stationary probability density model, yielding expressions for the transition probability and the stationary autocorrelation function. The analytical results have interpretative value for the mechanism of array SR, and may be of heuristic interest for applying array SR to related signal processing problems. Additionally, the analytical descriptions of an isolated bistable system agree well with numerical results of both conventional SR for a subthreshold rectangular input and residual SR for a slightly suprathreshold signal.
Weak-Periodic Stochastic Resonance in a Parallel Array of Static Nonlinearities
PLoS ONE, 2013
This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.
Array Enhanced Stochastic Resonance and Spatiotemporal Synchronization
Physical Review Letters, 1995
We enhance the response of a "stochastic resonator" by coupling it into a chain of identical resonators. Specifically, we show via numerical simulation that local linear coupling of overdamped nonlinear oscillators significantly enhances the signal-to-noise ratio of the response of a single oscillator to a time-periodic signal and noise. We relate this array enhanced stochastic resonance to the global spatiotemporal dynamics of the array and show how noise, coupling, and bistable potential cooperate to organize spatial order, temporal periodicity, and peak signal-to-noise ratio.
A new perspective on stochastic resonance in monostable systems
New Journal of Physics, 2010
Stochastic resonance induced by multiplicative white noise is theoretically studied in forced damped monostable oscillators. A stochastic amplitude equation is derived for the oscillation envelope, which has a linear stochastic resonance. This phenomenon is persistent when nonlinearities are considered. We propose three simple systems-a horizontally driven pendulum, a forced electrical circuit and a laser with an injected signal-that display this stochastic resonance. References 12
Enhancing array stochastic resonance in ensembles of excitable systems
Journal of Statistical Mechanics: Theory and Experiment, 2009
A summing network of FitzHugh-Nagumo model neurons, immersed in the background of both external noise and internal noise, is studied in the context of array stochastic resonance. An aperiodic Gaussian stimulus, assisted by collective internal array noise, stimulates the summing network for a more efficient response. This form of array stochastic resonance can be characterized by a correlation coefficient for an aperiodic input signal. Moreover, the correlation gain of the ensembles of neuronal models is investigated for finite and infinite array sizes. The nonmonotonic behavior of the correlation gain and the regions of the correlation gain beyond unity, i.e. the two main features of array SR, are demonstrated numerically and theoretically. These results suggest that certain levels of both external noise and internal noise contribute in a beneficial way to the neuronal coding strategy.
Stochastic resonance: numerical and experimental devices
Physica D: Nonlinear Phenomena, 2003
An array of overdamped bistable oscillators with delay was studied numerically. Each site of the array is coupled directionally with the addition of white Gaussian noise. On the other hand, we compared the results with an array of coupled chain of experimental devices, also fed with Gaussian white noise. We observed for an optimal amount of noise and moderated coupling good transmission along the line without degradation.
Stochastic resonance in finite arrays of bistable elements with local coupling
European Physical Journal B, 2009
In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective variable. By means of numerical simulations, the signal-to-noise ratio (SNR) and the gain are estimated as functions of the noise and the interaction coupling strength. A strong enhancement of the SR phenomenon for this collective variable in comparison with SR in single unit bistable systems is observed. Gains larger than unity are obtained for some parameter values and multi-frequency driving forces, indicating that the system is operating in a non-linear regime albeit the smallness of the driving amplitude. The large SNR values observed are basically due to the fact that the output fluctuations are small and short lived, in comparison with their typical values in a linear regime. A non-monotonic behavior of the SNR with the coupling strength is also obtained.
2006
We report the regions where a signal-to-noise ratio (SNR) gain exceeding unity exists in a parallel uncoupled array of identical bistable systems, for both subthreshold and suprathreshold sinusoids buried in broadband Gaussian white input noise. Due to independent noise in each element of the parallel array, the SNR gain of the collective array response approaches its local maximum exhibiting a stochastic resonant behavior. Moreover, the local maximum SNR gain, at a non-zero optimal array noise intensity, increases as the array size rises. This leads to the conclusion of the global maximum SNR gain being obtained by an infinite array. We suggest that the performance of infinite arrays can be closely approached by an array of two bistable oscillators operating in different noisy conditions, which indicates a simple but effective realization of arrays for improving the SNR gain. For a given input SNR, the optimization of maximum SNR gains is touched upon in infinite arrays by tuning both array noise levels and an array parameter. The nonlinear collective phenomenon of SNR gain amplification in parallel uncoupled dynamical arrays, i.e. array stochastic resonance, together with the possibility of the SNR gain exceeding unity, represent a promising application in array signal processing. *