Noise-induced order

Matsumoto, Kenji; Tsuda, Ichiro

doi:10.1007/bf01010923

Cited by 308 publications

(181 citation statements)

References 9 publications

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“…Some authors thus argue that there exists a phenomenon of noise-induced order [7], when at increasing the strength of the fluctuation σ, λ σ passes from positive to negative. Even the opposite phenomenon (noise-induced instability) has been observed: at increasing σ, λ σ can pass from negative to positive [5]- [6].…”

Section: Introductionmentioning

confidence: 99%

“…Usually [2,5,7], the degree of chaoticity is measured by treating the random term as a usual time-dependent term, and therefore, considering the separation of two nearby trajectories with the same realization of the noise. In this way it is possible to compute the maximum Lyapunov exponent λ σ associated to the separation rate of two nearby trajectories with the same realization of the stochastic term.…”

Section: Introductionmentioning

confidence: 99%

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Concept of complexity in random dynamical systems

1996

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We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. The meaning of K is discussed in the context of the information theory, and it is shown that it can be determined from real experimental data. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent λ σ computed considering two nearby trajectories evolving under the same randomness. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concept of complexity in random dynamical systems

1996

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“…It is well-known that in nonlinear dynamical systems, dynamical noise can induce a number of interesting phenomena, including stochastic resonance [32] (for a review, see [33]), noise-induced instability [34,35], noiseinduced order [36], noise-induced multistability [37], and noise-induced chaos [1][2][3][4][5][6][7][8]. The last is the most relevant to the recent criticisms on the noise titration technique, as one can ask: are the dynamics of the noisy maps considered in [28,29] simply stochastic or belong to noise-induced chaos?…”

Section: Introductionmentioning

confidence: 99%

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Gao¹,

Hu²,

Mao³

et al. 2012

Chaos, Solitons & Fractals

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a b s t r a c tDistinguishing low-dimensional chaos from noise is an important issue in time series analysis. Among the many methods proposed for this purpose is the noise titration technique, which quantifies the amount of noise that needs to be added to the signal to fully destroy its nonlinearity. Two groups of researchers recently have questioned the validity of the technique. In this paper, we report a broad range of situations where the noise titration technique fails, and offer solutions to fix the problems identified.

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“…Even if the content this observation appears trivial it is often ignored in literature. For example, most frequently it is used a definition of complexity which considers the separation of nearby trajectories [1][2][3] under the same realization of the noise. This definition implicitly assumes that the realization is known and should not be used when the contrary happens, has often it is.…”

mentioning

confidence: 99%

“…This definition implicitly assumes that the realization is known and should not be used when the contrary happens, has often it is. For example, the phenomenon of noise induced order [3] should be not considered a reduction of complexity when the random disturbance is non measurable.…”

mentioning

confidence: 99%

Random dynamical systems, entropies and information

Serva

2001

Physica A: Statistical Mechanics and its Applications

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Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is complex. Nevertheless, even according to this restricted definition, a general consensus on what should be the correct indicator for complexity is still not reached. In particular, this characterization is still lacking for systems whose time evolution is influenced by factors which are not under control and appear as random parameters or random noise. We show in this paper how to find the correct indicators for complexity in the information theory context. The crucial point is that the answer is twofold depending on the fact that the random parameters are measurable or not. The content of this apparently trivial observation has been often ignored in literature leading to paradoxical results. Predictability is obviously larger when the random parameters are measurable, nevertheless, in the contrary case, predictability improves when the unknown random parameters are time correlated.In a number of systems the dynamics is influenced by uncontrolled parameters which are intrinsically random or cannot be predicted with necessary precision. The evolution of a system of this type is described in the framework of random dynamical systems, word which indicates in the present paper also dynamical systems with noise.A dynamical system can be eventually studied by means of the associated symbolic dynamics, which, in this case, correspond to a stochastic process with random conditional probabilities, i.e. probabilities which depend on the same stochastic parameters.The obvious thing is that the possibility of forecasting the future evolution strongly depends on the possibility of measuring the parameters. The same model will have a different complexity (predictability) according to the fact that the measure is feasible or not. Even if the content this observation appears trivial it is often ignored in literature. For example, most frequently it is used a definition of complexity which considers the separation of nearby trajectories [1][2][3] under the same realization of the noise. This definition implicitly assumes that the realization is known and should not be used when the contrary happens, has often it is. For example, the phenomenon of noise induced order [3] should be not considered a reduction of complexity when the random disturbance is non measurable.A better characterization of complexity for dynamical systems with unmeasurable randomness has been recently found out for many physically relevant cases [4][5][6][7].In this paper we show how to find proper indicators of complexity in the two cases of measurable (accessible information) and non measurable (inaccessible information) randomness. We also show, with an example, that in case the stochastic parameters have memory, part of the inaccessible information is encoded in the dynamics of the system and can be recovered. In other words,

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Noise-induced order

Cited by 308 publications

References 9 publications

Concept of complexity in random dynamical systems

Concept of complexity in random dynamical systems

Detecting low-dimensional chaos by the “noise titration” technique: Possible problems and remedies

Random dynamical systems, entropies and information

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