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| 001 | 978-3-319-47837-1 | ||
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| 005 | 20220801222615.0 | ||
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| 008 | 161215s2017 sz | s |||| 0|eng d | ||
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_a10.1007/978-3-319-47837-1 _2doi |
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| 100 | 1 |
_aElaskar, Sergio. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _962362 |
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| 245 | 1 | 0 |
_aNew Advances on Chaotic Intermittency and its Applications _h[electronic resource] / _cby Sergio Elaskar, Ezequiel del Río. |
| 250 | _a1st ed. 2017. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2017. |
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| 300 |
_aXVIII, 197 p. 99 illus., 62 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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| 505 | 0 | _aChapter 1: Introduction to chaotic intermittency -- Chapter 2: Other types of intermittency and some recent advances in the study of chaotic intermittency -- Chapter 3: Some applications of the chaotic Intermittency -- Chapter 4: Classical theory about noise effects in chaotic intermittency -- Chapter 5: New formulation of the chaotic intermittency -- Chapter 6: New formulation of the noise effects in chaotic intermittency -- Chapter 7: Application of the new formulation to pathological cases -- Chapter 8: Application to dynamical systems. An example with discontinuous RPD: the derivative nonlinear Schrodinger equation -- Chapter 9: Evaluation of the intermittency statistical properties using the Perron-Frobenius operator. | |
| 520 | _aOne 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 intermittency type, 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. . | ||
| 650 | 0 |
_aMechanics, Applied. _93253 |
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| 650 | 0 |
_aContinuum mechanics. _93467 |
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| 650 | 0 |
_aMathematical physics. _911013 |
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| 650 | 0 |
_aDynamics. _962363 |
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_aNonlinear theories. _93339 |
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_aElectrical engineering. _962364 |
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| 650 | 0 |
_aNeurosciences. _924499 |
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| 650 | 1 | 4 |
_aEngineering Mechanics. _931830 |
| 650 | 2 | 4 |
_aContinuum Mechanics. _93467 |
| 650 | 2 | 4 |
_aMathematical Physics. _911013 |
| 650 | 2 | 4 |
_aApplied Dynamical Systems. _932005 |
| 650 | 2 | 4 |
_aElectrical and Electronic Engineering. _962365 |
| 650 | 2 | 4 |
_aNeuroscience. _934310 |
| 700 | 1 |
_adel Río, Ezequiel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _962366 |
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| 710 | 2 |
_aSpringerLink (Online service) _962367 |
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| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783319478364 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783319478388 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783319838366 |
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-47837-1 |
| 912 | _aZDB-2-ENG | ||
| 912 | _aZDB-2-SXE | ||
| 942 | _cEBK | ||
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_c80956 _d80956 |
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