Distinguishing Noise from Chaos

Rosso, Osvaldo A.; Larrondo, H.A.; Martín, María Teresa; Plastino, A.; Fuentes, Miguel

doi:10.1103/physrevlett.99.154102

Cited by 609 publications

(677 citation statements)

References 23 publications

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“…On the contrary, the value of C increases for increasing τ in the range τ = 2..80 ns, reaches a maximum at τ = 80 ns, and decreases for longer τ . Previous works have shown that the correlations present in deterministic chaotic systems typically yield intermediate values of H ranging from 0.45 to 0.75 and values of C near the maximum, which is C = 0.5 for D = 6 [8]. This means that correlated dynamics is found to dominate in the range τ = 14..120 ns in our experimental realization.…”

supporting

confidence: 49%

“…To distinguish between these two components we propose, in this letter, to use quantifiers derived from information theory. In particular, permutation entropy and statistical complexity [8] are good candidates for this task. They have already shown to be successful in identifying the internal structures of time series originated from delay systems [9,10].…”

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confidence: 99%

“…The H − C plane was introduced in [8] to distinguish between the deterministic chaotic and stochastic nature of a time series. The inset of Fig.…”

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confidence: 99%

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Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

et al. 2011

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In the dynamics of optical systems one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important although difficult task. Often the time scales at which determinism and noise dominate the system's dynamics differ. In this letter we propose to use information-theory-derived quantifiers, more precisely permutation entropy and statistical complexity, to distinguish between the two behaviors. Based on experiments of a paradigmatic optoelectronic oscillator we demonstrate that the time scales at which deterministic or noisy behavior dominate can be identified. Supporting numerical simulations prove the accuracy of this identification. c 2011 Optical Society of America OCIS codes: 140.1540, 190.3100, 250.5960, 000.5490. Delayed coupling phenomena play an important role in optical systems, including semiconductor lasers with feedback [1], delay-coupled lasers [2], and optoelectronic oscillators [3]. In particular, the latter have proven to be practical benchmark systems to study delay dynamics [3,4]. Moreover, these oscillators have turned out to be versatile systems for novel applications such as chaos communications [5] or generation of ultra-high spectral purity microwaves [6]. The main dynamical features of this test-bed system are well documented and characterized, both from the theoretical and the experimental point of view [7]. Experimental realizations of the optoelectronic oscillator are usually affected by an unpredictable stochastic component. In particular, when the dynamical system is driven into the hyperchaotic regime, it can be hard to distinguish between the deterministic chaotic dynamics and the stochastic component when they coexist. To distinguish between these two components we propose, in this letter, to use quantifiers derived from information theory. In particular, permutation entropy and statistical complexity [8] are good candidates for this task. They have already shown to be successful in identifying the internal structures of time series originated from delay systems [9,10].To compute these quantifiers, we analyze the time series of the system's dynamics and from them construct a probability distribution of their amplitudes. We choose the Bandt and Pompe method due to its simplicity and effectiveness [11]. Band and Pompe consider the order of neighboring values, by comparing their amplitude values, rather than partitioning the amplitude into different levels. This avoids amplitude threshold sensitivity dependences. The probability distribution of the generated ordinal pattern for a given time series can be established once an embedding dimension D and an embedding delay time τ are chosen. The embedding dimension D refers to the number of symbols that forms the ordinal pattern. The embedding delay τ is the time separation between symbols which is directly related to the sampling time of the time series (see refs. [9-11] for a detailed derivation and description of the quantifiers). Fig. 1. The optoel...

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Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

et al. 2011

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“…It was originally proposed and assessed for one-dimensional signals, for which it was shown to be able to detect transition points between different regimes [18]. This feature is the product of an entropy and a stochastic distance between the model which best describes the data and an equilibrium distribution [12,13].…”

Section: Introductionmentioning

confidence: 99%

Generalized Statistical Complexity of SAR Imagery

Almeida

Medeiros

Rosso

et al. 2012

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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Abstract.A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso et al in 2010. It is a functional that captures the notions of order/disorder and of distance to an equilibrium distribution. The former is computed by a measure of entropy, while the latter depends on the definition of a stochastic divergence. When the scene is illuminated by coherent radiation, image data is corrupted by speckle noise, as is the case of ultrasound-B, sonar, laser and Synthetic Aperture Radar (SAR) sensors. In the amplitude and intensity formats, this noise is multiplicative and non-Gaussian requiring, thus, specialized techniques for image processing and understanding. One of the most successful family of models for describing these images is the Multiplicative Model which leads, among other probability distributions, to the G 0 law. This distribution has been validated in the literature as an expressive and tractable model, deserving the "universal" denomination for its ability to describe most types of targets. In order to compute the statistical complexity of a site in an image corrupted by speckle noise, we assume that the equilibrium distribution is that of fully developed speckle, namely the Gamma law in intensity format, which appears in areas with little or no texture. We use the Shannon entropy along with the Hellinger distance to measure the statistical complexity of intensity SAR images, and we show that it is an expressive feature capable of identifying many types of targets.

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“…Complexity measures have been shown to be powerful tools for detecting dynamical changes in time series from epileptic patients [27] and in speech signals [20,28], for distinguishing chaotic signals from stochastic ones, for distinguishing among different degrees of stochasticity [29], for quantifying stochastic and coherence resonances [30], and for classifying spatio-temporal patterns [31,32] and neural networks [33,34] etc.…”

Section: Introductionmentioning

confidence: 99%

Quantifying the complexity of the delayed logistic map

Masoller

Rosso

2011

Phil. Trans. R. Soc. A.

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Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the 'histogram-based' probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of the delay-induced dynamics: there are parameter regions where the histogram-based complexity is zero while the ordinal pattern complexity is not, and vice versa. We also show that the time series generated from the nonlinear delayed logistic map can present zero missing or forbidden patterns, i.e. all possible ordinal patterns are realized into orbits.

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Distinguishing Noise from Chaos

Cited by 609 publications

References 23 publications

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

Generalized Statistical Complexity of SAR Imagery

Quantifying the complexity of the delayed logistic map

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