Overview
- Contributes to the state-of-the-art knowledge about chaotic intermittency
- Develops three new methodologies to evaluate the reinjection mechanism, with several examples to verify them
- Permits to evaluate the statistical properties of chaotic intermittency
- Equips readers with new tools to understand chaotic intermittency
- Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data.
As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittencytype, is now a function depending on the whole map, not just on the local map. Also, a new analytical approach to obtain the RPD from the mathematical expression of the map is presented. In this way all cases of non standard intermittencies are included in the same frame work.
This methodology is extended to evaluate the noisy reinjection probability density function (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. This is an important difference with respect to the classical approach based on the Fokker-Plank equation or Renormalization Group theory, where the noise effect was usually considered just on the local Poincaré map.
Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. Along the book examples of applications are described, which have shown very good agreement with numerical computations.
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Authors and Affiliations
About the authors
Prof. Dr. Ezequiel del Rio is graduated in Physical Sciences (1987) and Doctor in Physical Sciences atthe Complutense University of Madrid (1993). He is currently Professor at the Polytechnic University of Madrid (from 1993). He is co-author of many books and more than 100 refereed publications in journals and conference proceedings. At the present, del Rio is Co-Director of the Doctorate of Engineering Sciences at the Aerospace School of the Polytechnic University of Madrid. His main fields of investigation are related with chaos, complex systems and stochastic systems.
Bibliographic Information
Book Title: New Advances on Chaotic Intermittency and its Applications
Authors: Sergio Elaskar, Ezequiel del Río
DOI: https://doi.org/10.1007/978-3-319-47837-1
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-47836-4Published: 28 December 2016
Softcover ISBN: 978-3-319-83836-6Published: 07 July 2018
eBook ISBN: 978-3-319-47837-1Published: 14 December 2016
Edition Number: 1
Number of Pages: XVIII, 197
Number of Illustrations: 37 b/w illustrations, 62 illustrations in colour
Topics: Theoretical and Applied Mechanics, Fluid- and Aerodynamics, Mathematical Applications in the Physical Sciences, Complexity, Electrical Engineering, Neurosciences