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New Advances on Chaotic Intermittency and Its Applications (Hardcover) (Sergio Elaskar & Ezequiel Del
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In thisbook, research including new methodologies to investigate systems showingchaotic intermittency phenomenon is presented. A new general methodology toevaluate the reinjection probability density function (RPD) is developed inChapters 4 to 7. The key of this formulation is the introduction of a newfunction, called M(x), which is utilized to calculate the RPD function in placeto consider the huge number of numerical or experimental data. The functionM(x) depends on two integrals, this characteristic reduces the influence on thestatistical fluctuations in the data series. Also, the function M(x) is easy toevaluate from the data series.Thismethodology is extended to evaluate the noisy reinjection probability density(NRPD), the noisy probability of the laminar length and the noisycharacteristic relation. In Chapter 8, we present a new theoretical approach toobtain the RPD directly from the analytical expression of the map. EstimatedRPD enables analytic evaluation of the characteristic exponent traditionallyused to characterize the intermittency type. The proposed theoretical method isgeneral and very simple to use. Finally,in Chapter 9, a new scheme to evaluate the RPD function using thePerron-Frobenius operator is developed. In fact, the analytical RPD functions,obtained with these three methodologies, are more general than the previousones; and the classical uniform reinjection is only a particular case. The RPDfunctions and other statistical variables of intermittency, calculated usingthe three new methodologies, are compared with numerical computations showingvery good agreement.