Optoelectronic Chaotic Circuits

Hanias, M. P.; Nistazakis, H. E.; Tombras, George S.

doi:10.5772/15598

Cited by 4 publications

(4 citation statements)

References 15 publications

(13 reference statements)

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“…For the computation of these two geometric invariants, the time delay

and embedding dimension p are essential parameters, and a bad selection of them would produce a big bias in

and

. The largest Lyapunov exponent

for the five systems have been computed in [ 27 , 32 , 33 , 34 , 35 ] and the Correlation Dimension

in [ 32 , 33 , 36 , 37 ]. Furthermore, we have completed the study by increasing the sample size to 10,000 observations.…”

Section: Simulation Analysismentioning

confidence: 99%

“…These complexity measures are the largest Lyapunov exponent LLE [30], which is a measure of the complexity of the time process, and the Correlation Dimension D [31], which is a measure of the dimension of the space occupied by the chaotic attractor. For the computation of these two geometric invariants, the time delay τ * and embedding dimension p are essential parameters, and a bad selection of them would produce a big bias in LLE and D. The largest Lyapunov exponent LLE for the five systems have been computed in [27,[32][33][34][35] and the Correlation Dimension D in [32,33,36,37]. Furthermore, we have completed the study by increasing the sample size to 10,000 observations.…”

mentioning

confidence: 99%

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Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Matilla-García

Morales

Rodríguez

et al. 2021

Entropy

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The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ* and embedding dimension p for phase space reconstruction. The value of τ* can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ* should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ*, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ*. In this paper, we suggest a simple method for estimating τ* and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ* is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

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“…For the computation of these two geometric invariants, the time delay

and embedding dimension p are essential parameters, and a bad selection of them would produce a big bias in

and

. The largest Lyapunov exponent

for the five systems have been computed in [ 27 , 32 , 33 , 34 , 35 ] and the Correlation Dimension

in [ 32 , 33 , 36 , 37 ]. Furthermore, we have completed the study by increasing the sample size to 10,000 observations.…”

Section: Simulation Analysismentioning

confidence: 99%

mentioning

confidence: 99%

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Matilla-García

Morales

Rodríguez

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…The slope D 2 which gives an estimate of the correlation dimension is a characteristic quantity for time series and it shows how the correlation sum, Cr, scales with r. The slope of the linear section of the log(Cr) versus log(r) plot presents the important information required for characterization of the phase space attractor [18]. The slope of the log(Cr) versus log(r) plot can be estimated by the least square fit method of a straight line also termed as a scaling region over a certain range of hypespherical radius, r. The hyperspherical radius, r, is a radius interval of sufficient length for small r where the dimension D 2 remains approximately constant and regarded as an estimate of the correlation dimension [19].…”

Section: Scaling Regionmentioning

confidence: 99%

Mapping the Wall-Region Dynamics of High-Flux Gas-Solid Riser Using Scaling Regions from the Solid Concentration Time Series

Jeremiah¹,

Manyele²,

Temu³

et al. 2019

ENG

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An experimental study of the gas-solid flow dynamics in the high-flux CFB riser was accomplished by analysing the scaling regions from solid concentration signals collected from a 76 mm internal diameters and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m 2 s solids flux. Spent fluid catalytic cracking (FCC) catalyst particles of 67 µm mean diameter and 1500 kg/m 3 density together with 70% to 80% humid air was used. Solid concentration data were analysed using codes prepared in FORTRAN 2008 to get correlation integrals at different embedding dimensions and operating conditions and plot their profiles. Scaling regions were identified by visual inspection method and their location on planes determined. Scaling regions were analysed based on operating conditions and riser spatial locations. It was found that scaling regions occupy different locations on the plane depending on the number of embedding dimensions and operating conditions. As the number of embedding dimensions increases the spacing between scaling regions decreases until it saturates towards higher embedding dimensions. Slopes of scaling regions increases with embedding dimensions until saturation where they become constant. Slopes of scaling regions towards the wall decrease while the number of scaling regions for a particular profile increases. The span of the scaling region is wider at the initial values of hyperspherical radius than its final values. The scaling regions in some flow development sections show multifractal behaviour for each embedding dimension which manifests into visible basin which is defined in this study as multifractal basin. Further, the end points of the scaling region for each correlation integral profile differ from each other as the embedding dimension changes. This study suggests that identification of scaling region by visual inspection How to cite this paper:

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“…Using the scaling region, D is the slope of ln(Cr) versus ln(r) plot. The slope D of the linear part of the log-log curve provides all necessary information for characterizing the attractor [16]. The slope is generally estimated by a least square fit of a straight line over a certain range of r called the scaling region, which is a radius interval of sufficient length at small r where D(r) remains approximately constant and regards this value as an estimate of D(r) [17].…”

Section: The Process Of Determining Correlation Dimension Involves Fimentioning

confidence: 99%

Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series

Jeremiah¹,

Manyele²,

Temu³

et al. 2018

ENG

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Analysis of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using embedded solid concentration time series collected from a 76 mm internal diameter and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s air velocity and 50 to 550 kg/m 2 s solids flux of spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m 3. Data were analyzed using prepared FORTRAN 2008 code to get correlation integral followed by determination of correlation dimensions with respect to the hyperspherical radius and their profiles, plots of which were studied. It was found that correlation dimension profiles at the centre have single peak with higher values than the wall region profiles. Towards the wall, these profiles have double or multiple peaks showing bifractal or multifractal flow behaviors. As the velocity increases the wall region profiles become random and irregular. Further it was found that, as the height increases the correlation dimension profiles shift towards higher hyperspherical radius at the centre and towards lower hyperspherical radius in the wall region at r/R = 0.81. The established method of mapping correlation dimension profiles in this study forms a suitable tool for analysis of high-flux riser dynamics compared to other analyses approaches. However, further analysis is recommended to other gas-solid CFB riser of different dimensions operated at high-flux conditions using the established method.

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Optoelectronic Chaotic Circuits

Cited by 4 publications

References 15 publications

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Mapping the Wall-Region Dynamics of High-Flux Gas-Solid Riser Using Scaling Regions from the Solid Concentration Time Series

Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series

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