Nonuniform reinjection probability density function in type V intermittency

Elaskar, Sergio; Río, Ezequiel del; Marcantoni, Luis Felipe Gutierrez

doi:10.1007/s11071-018-4083-7

Cited by 9 publications

(15 citation statements)

References 37 publications

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“…It includes the uniform reinjection as a particular case, and it has shown to be very accurate for a broad class of maps showing type I, II, and III intermittencies [4,[25][26][27][28][29][30][31][32][33][34][35]. This methodology has been recently applied to type V intermittency obtaining continuous and nonuniform RPDs [36]. In this paper, we implement the M function methodology to describe discontinuous RPD functions for type V intermittency.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Reinjection Probability Density functions in Type V Intermittency

Elaskar

Río

2018

Journal of Computational and Nonlinear Dynamics

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This paper reports theoretical and numerical results about the reinjection process in type V intermittency. The M function methodology is applied to a simple mathematical model to evaluate the reinjection process through the reinjection probability density function (RPD), the probability density of laminar lengths, and the characteristic relation. We have found that the RPD can be a discontinuous function and it is a sum of exponential functions. The RPD shows two reinjection behaviors. Also, the probability density of laminar lengths has two different behaviors following the RPD function. The dependence of the RPD function and the probability density of laminar lengths with the reinjection mechanisms and the lower boundary of return are considered. On the other hand, we have obtained, for the analyzed map, that the characteristic relation verifies l¯≈ε−0.5. Finally, we highlight that the M function methodology is a suitable tool to analyze type V intermittency and there is a very high accuracy between the new theoretical equations and the numerical data.

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Section: Introductionmentioning

confidence: 99%

Discontinuous Reinjection Probability Density functions in Type V Intermittency

Elaskar

Río

2018

Journal of Computational and Nonlinear Dynamics

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“…We emphasize that as the number of reinjected points increases, the accuracy of the density technique and the M function methodology increases too. In addition, we note that the errors generated by Equation (32) are lower than those obtained from Equation (34). On the other hand, the M function methodology obtains α ≈ 0.9056.…”

Section: Resultsmentioning

confidence: 68%

“…A detailed explanation of the M function methodology can be found in Refs. [3,[29][30][31][32][33][34][35]. The RPD calculated using the M function methodology results…”

Section: Resultsmentioning

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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“…Let us introduce the following map [38] in equation ( 27) (see below), where F (x m ) = y m = 1, x is the lower boundary of reinjection, and ε is the control parameter. This map has a fixed point x = 0 for ε = 0.…”

Section: Case 1 Type V Intermittency With Overlapping In the Lower Pa...mentioning

confidence: 99%

Chaotic intermittency with non-differentiable M(x) function

Elaskar¹,

Río

Grioni

2023

Rev.Fac.Ing.Univ.Antioquia

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One-dimensional maps showing chaotic intermittency with discontinuous reinjection probability density functions are studied. For these maps, the reinjection mechanism possesses two different processes. The M function methodology is applied to analyze the complete reinjection mechanism and to determine the discontinuous reinjection probability density function. In these maps, the function M(x) is continuous and non-differentiable. Theoretical equations are found for the function M(x) and for the reinjection probability density function. Finally, the theoretical results are compared with numerical data finding high accuracy.

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Nonuniform reinjection probability density function in type V intermittency

Cited by 9 publications

References 37 publications

Discontinuous Reinjection Probability Density functions in Type V Intermittency

Discontinuous Reinjection Probability Density functions in Type V Intermittency

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

Chaotic intermittency with non-differentiable M(x) function

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