Array Enhanced Stochastic Resonance and Spatiotemporal Synchronization

Lindner, John F.; Meadows, Brian K.; Ditto, William L.; Inchiosa, Mario A.; Bulsara, Adi R.

doi:10.1103/physrevlett.75.3

Cited by 431 publications

(233 citation statements)

References 14 publications

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“…3. The qualitative correspondence is good; moreover, the maxima of the curves are rather good reproduced with the formula (6).…”

supporting

confidence: 49%

“…Stochastic resonance has been observed in numerous experiments [3]. Noteworthy, the order in a noise-driven system can have a maximum at a certain noise level even in the absence of periodic forcing, this phenomenon being called coherence resonance [4].Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems.…”

mentioning

confidence: 99%

“…Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems.…”

mentioning

confidence: 99%

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System Size Resonance in Coupled Noisy Systems and in the Ising Model

2002

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We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles -lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance. DOI: 10.1103/PhysRevLett.88.050601 PACS numbers: 05.40.Ca, 05.45. -a, 05.50. +q Stochastic resonance has attracted much interest recently [1]. As was demonstrated in [2], a response of a noisy nonlinear system to a periodic forcing can exhibit a resonancelike dependence on the noise intensity. In other words, there exists a "resonant" noise intensity at which the response to a periodic force is maximally ordered. Stochastic resonance has been observed in numerous experiments [3]. Noteworthy, the order in a noise-driven system can have a maximum at a certain noise level even in the absence of periodic forcing, this phenomenon being called coherence resonance [4].Being first discussed in the context of a simple bistable model, stochastic resonance has been also studied in complex systems consisting of many elementary bistable cells [5]; moreover, the resonance may be enhanced due to coupling [6]. In this paper we discuss another type of resonance in such systems, namely, the system size resonance, when the dynamics is maximally ordered at a certain number of interacting subsystems. Contrary to previous reports of array-enhanced stochastic resonance (cf. also [7]), here we fix the noise strength, coupling, and other parameters; only the size of the ensemble changes.The basic model to be considered below is the ensemble of noise-driven bistable overdamped oscillators, governed by the Langevin equations,Here j i ͑t͒ is a Gaussian white noise with zero mean: ͗j i ͑t͒j j ͑t 0 ͒͘ d ij d͑t 2 t 0 ͒;´is the coupling constant; N is the number of elements in the ensemble, and f͑t͒ is a periodic force to be specified later. In the absence of periodic force, the model (1) has been extensively studied in the thermodynamic limit N !`. It demonstrates an Isingtype phase transition at´´c from the disordered state with vanishing mean field X N 21 P i x i to the "ferromagnetic" state with a nonzero mean field X 6X 0 [8].While in the thermodynamic limit the full description of the dynamics is possible, for finite system sizes we have mainly a qualitative picture: In the ordered phase the mean field X switches between the values 6X 0 and its average vanishes for all couplings. The rate of switchings depends on the system size and tends to zero as N !`.For us, the main importance is the fact that qualitatively the behavior of the mean...

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“…3. The qualitative correspondence is good; moreover, the maxima of the curves are rather good reproduced with the formula (6).…”

supporting

confidence: 49%

mentioning

confidence: 99%

mentioning

confidence: 99%

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System Size Resonance in Coupled Noisy Systems and in the Ising Model

2002

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“…Therefore, an optimal amount of multiplicative noise is required to support the bistable structure. Nothing similar occurs in array-enhanced SR [24] or in SR in extended bistable systems [25]. On the other hand, an increase of additive noise also leads to a loss of bistability (see Fig.…”

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confidence: 98%

Noise Induced Propagation in Monostable Media

et al. 2001

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We show that external fluctuations are able to induce propagation of harmonic signals through monostable media. This property is based on the phenomenon of doubly stochastic resonance, where the joint action of multiplicative noise and spatial coupling induces bistability in an otherwise monostable extended medium, and additive noise resonantly enhances the response of the system to a harmonic forcing. Under these conditions, propagation of the harmonic signal through the unforced medium is observed for optimal intensities of the two noises. This noise-induced propagation is studied and quantified in a simple model of coupled nonlinear electronic circuits.

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“…The corresponding SNR curves are also shown in the middle plot. From Lindner et al, 1995. deed what happens. Figure 30 shows the dependence of the maximum SNR on the coupling strength for different system sizes, as measured experimentally by Löcher et al ͑1996͒ in a linear array of bistable diode resonators.…”

Section: A Discrete Arraysmentioning

confidence: 99%

Spatiotemporal order out of noise

2007

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Natural systems are undeniably subject to random fluctuations, arising from either environmental variability or thermal effects. The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels. It is known that, under these conditions, noisy fluctuations can interact with the system's nonlinearities to render counterintuitive behavior, in which an increase in the noise level produces a more regular behavior. In systems with spatial degrees of freedom, this regularity takes the form of spatiotemporal order. An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described resulting from these effects. The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential equations. Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

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Array Enhanced Stochastic Resonance and Spatiotemporal Synchronization

Cited by 431 publications

References 14 publications

System Size Resonance in Coupled Noisy Systems and in the Ising Model

System Size Resonance in Coupled Noisy Systems and in the Ising Model

Noise Induced Propagation in Monostable Media

Spatiotemporal order out of noise

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