Experimental evidence for dichotomous noise-induced states in a bistable interference filter

Broussell, I.; L’Heureux, Ivan; Fortin, E.

doi:10.1016/s0375-9601(96)00860-2

Cited by 13 publications

(9 citation statements)

References 15 publications

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“…[40][41][42][43][44][45][46][47][48] Also, from the experimental point of view, it is possible to¯nd the evidently presence of the dichotomous noise. 40,[49][50][51] The application of symmetric dichotomous noise to the Anderson model has demonstrated the absence of metalinsulator transition, namely, there is no extended states in the thermodynamic limit. [52][53][54] To know about the localization properties of the disordered direct TLs, we study the behavior of the normalized localization length Ãð!…”

Section: Introductionmentioning

confidence: 99%

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

Lazo

Humire

Saavedra

2014

Int. J. Mod. Phys. C

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In this work we study the localization properties of diluted and nondiluted disordered direct transmission lines (TLs), when we distribute two values of inductances, L A and L B , according to an asymmetric dichotomous sequence. Using the scaling properties of the participation number D we study the localization properties in the thermodynamic limit. For certain and parameter speci¯c values, which characterize the dichotomous noise, we have found the following limit conditions: lim !1 mð!; ; Þ ! 1:0 or lim !1 mð!; ; Þ ! 1:0, for the appearing of the disorder-order transitions. Here mð!; ; Þ are the slopes of the linear relationships between lnðDÞ and lnðNÞ. In addition, in each ! c resonance frequency generated by the dilution process we demonstrate the existence of extended intermediate states in the thermodynamic limit.

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Section: Introductionmentioning

confidence: 99%

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

Lazo

Humire

Saavedra

2014

Int. J. Mod. Phys. C

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“…(1) can serve as a case study of a nonlinear system driven by a correlated noise [3]; it has also been studied in the context of stochastic synchronization [11]; it may, furthermore, also be regarded as a model for two bistable systems being unidirectionally coupled (such systems have been studied in the context of noise-mediated patterns [12]). Possible experimental realizations include noisy electronic circuits [13], flux gate magnetometers [12], and bistable interference filters [14].…”

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confidence: 99%

Correlations in the Sequence of Residence Times

Lindner

Schwalger

2007

Phys. Rev. Lett.

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Sequences of residence times (RTs) associated with the escape from metastable states are observed in many fields. Here we study analytically and numerically the correlations among RTs for a bistable stochastic system driven by dichotomous noise. Our theory predicts an oscillatory behavior of the correlations with respect to the lag between RTs. Correlations vanish at all lags if the switching rate matches the hopping rate of the unperturbed system. It is also shown that RT correlations may reveal features of the driving which are not present in the single-RT statistics. Not much attention has been paid to the fact that RTs are most naturally observed in sequences: the subsequent epochs spent by a Brownian particle in the left and right wells of a quartic potential, the time spent in the neighboring minima of a periodic potential, or the periods spent near the resting state of an excitable system [7]-all of these residence times are commonly measured (in experiments or in a model simulation) as an ordered sequence fI k g, with k 0; 1; . . . . These RTs will be only in the most simple cases mutually independent. In any case involving external driving, inertia, delayed feedback, etc., we expect that RT correlations will emerge. Except for certain neuron models where sequences of interspike intervals correspond to sequences of first-passage times [8][9][10], however, such correlations in the RT sequence have not been studied to the best of our knowledge.In this Letter, we study RT correlations in a simple setup that is analytically tractable. For a bistable system driven by a thermal and by a dichotomous noise, the standard statistics of the RT (i.e., the RT density) will be contrasted with the surprising features of the RT correlation statistics. We show that, besides the expected behavior of correlations at the small switching rate of the dichotomous driving, we find nonintuitive effects such as the vanishing of linear correlations when the driving's switching rate matches the unperturbed escape rate of the system and an inversion of the RT correlation's sign for an even larger switching rate of the driving. We also demonstrate how input parameters can be inferred from the RT correlations if the driving is slow and weak.We consider the dynamics of an overdamped bistable system driven by a dichotomous (telegraph) noise:

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“…(21). Due to the asymmetric case under consideration, there exists a particular choice of parameters such that a coefficient of the two deltas vanishes.…”

Section: P-3mentioning

confidence: 99%

“…Furthermore, by an appropriate procedure of limit the dichotomic noise converges at the Gaussian white noise as the Ornstein-Uhlenbeck does, and it also converges at the white shot noise [19]. Experimental evidences of the dichotomic noise have been found frequently in the litterature [5,[20][21][22]. In Ref.…”

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confidence: 99%

An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

Aquino¹,

Bologna²,

Calisto³

2010

Europhys. Lett.

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Abstract. -Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics.Introduction. -In this letter we focus our attention on a growth model that was first used to describe the statistical behavior of a population of individual species; for example, human population growth. This is an area of interest several centuries old and is perhaps one of the oldest branches of biology to be studied quantitatively. The first model for human population growth was proposed by Malthus in 1798. In 1838 Verhulst [1] corrected this first model taking into account both the limitation of the growth of a population due to the competition between individuals, and the limitation on the density of the population that the environment can support. An example of this would be the limitation on the amount of food that the system is capable of producing. The proposed equation is known as the logistic equation,ẋ = a 0 x(1 − x).There are many examples of assemblies that consist of a number of elements that interact through cooperative or competitive mechanisms. Some important examples include species that share a given environment, such as animals that live in the seas and rivers of our planet; the components of the central nervous system of a living being; transmission of diseases caused by different types of viruses; interacting vortices in a turbulent fluid; coupled

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Experimental evidence for dichotomous noise-induced states in a bistable interference filter

Cited by 13 publications

References 15 publications

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

Correlations in the Sequence of Residence Times

An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

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