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New Advances on Chaotic Intermittency and its Applications (Paperback, Softcover reprint of the original 1st ed. 2017)
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New Advances on Chaotic Intermittency and its Applications (Paperback, Softcover reprint of the original 1st ed. 2017)
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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 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 Poincare
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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