New Advances on Chaotic Intermittency and its Applications

In this book, research including new methodologies to investigate systems showing chaotic intermittency phenomenon is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 4 to 7. The key of this formulation is the introduction of a new function, called M(x), which is utilized to calculate the RPD function in place to consider the huge number of numerical or experimental data. 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. This methodology is extended to evaluate the noisy reinjection probability density (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. In Chapter 8, we present a new theoretical approach to obtain the RPD directly from the analytical expression of the map. Estimated RPD enables analytic evaluation of the characteristic exponent traditionally used to characterize the intermittency type. The proposed theoretical method is general and very simple to use. Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. In fact, the analytical RPD functions, obtained with these three methodologies, are more general than the previous ones; and the classical uniform reinjection is only a particular case. The RPD functions and other statistical variables of intermittency, calculated using the three new methodologies, are compared with numerical computations showing very good agreement.