New Advances on Chaotic Intermittency and its Applications

Río, Ezequiel del; Elaskar, Sergio

doi:10.1007/978-3-319-47837-1

Cited by 27 publications

(39 citation statements)

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“…Note that Equation (1) supposes that F(x) is differentiable and invertible with con- [39]. On the other hand, the theoretical formulation of the M function methodology requires that [3,30]. Let us now introduce a map y = F(x), which is piecewise differentiable and satisfies |F (x)| = 0, except in a finite number of critical points.…”

Section: The Perron-frobenius Operatormentioning

confidence: 99%

“…The weight w is included because it is current to normalize the RPD function over the laminar interval I L as I L φ(x)dx = 1. Therefore, to obtain the RPD function, the sum in Equation (2) must exclude the contributions that do not generate reinjection in the laminar zone [3,40]…”

Section: Evaluation Of the Rpdmentioning

confidence: 99%

“…The laminar phases, also called regular phases, are related to pseudo-equilibrium regions or pseudo-periodic solutions. The bursts correspond to chaotic behavior [1][2][3][4]. Intermittency has been observed in engineering, physics, medicine, chemistry, and economy [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…One-dimensional maps are widely used to study chaotic intermittency [1][2][3][4]. These maps have a mechanism to reinject the trajectories from the chaotic region to the laminar one, which determines the reinjection probability density (RPD) function [1,3]. The RPD function describes the probability of the trajectories to be reinjected at each point of the laminar interval.…”

Section: Introductionmentioning

confidence: 99%

“…To calculate this general RPD, the M function methodology was developed, which has worked accurately for maps with types I, II, III and V intermittencies without and with noise. The M function methodology uses a less restrictive assumption of a constant density at points that govern the reinjection process, i.e., pre-reinjection points [3,[26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

2021

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We use the natural invariant density of the map and the Perron–Frobenius operator to analytically evaluate the statistical properties for chaotic intermittency. This study can be understood as an improvement of the previous ones because it does not introduce assumptions about the reinjection probability density function in the laminar interval or the map density at pre-reinjection points. To validate the new theoretical equations, we study a symmetric map and a non-symmetric one. The cusp map has symmetry about x=0, but the Manneville map has no symmetry. We carry out several comparisons between the theoretical equations here presented, the M function methodology, the classical theory of intermittency, and numerical data. The new theoretical equations show more accuracy than those calculated with other techniques.

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Section: The Perron-frobenius Operatormentioning

confidence: 99%

Section: Evaluation Of the Rpdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

2021

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Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Pancóatl‐Bortolotti,

Enríquez‐Caldera,

Costa

et al. 2023

Numer Methods Biomed Eng

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The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol – Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi‐chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi‐chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine‐tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non‐stationary signals while reconstructing the time‐frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal‐to‐noise ratio (SNR) of −10 dB. Furthermore, compared to other time‐frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio‐thermal effects.

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Crisis-Induced Intermittency and Other Nonlinear Dynamics Phenomena in Vibro-impact System with Soft Impact

Баженов

Pogorelova

Postnikova

2021

Advanced Structured Materials

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New Advances on Chaotic Intermittency and its Applications

Cited by 27 publications

References 0 publications

Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Crisis-Induced Intermittency and Other Nonlinear Dynamics Phenomena in Vibro-impact System with Soft Impact

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