NEW ADVANCES ON CHAOTIC INTERMITTENCY AND APPLICATIONS

DEL RIO, EZEQUIEL; ELASKAR, SERGIO

Springer

Año: 2016 p. 215

978-3-319-47836-4

p { margin-bottom: 0.21cm; direction: ltr; color: rgb(0, 0, 10); line-height: 120%; text-align: left; widows: 2; orphans: 2; }p.western { font-family: "Calibri",serif; font-size: 11pt; }p.cjk { font-family: "Droid Sans Fallback"; font-size: 11pt; }p.ctl { font-family: "Calibri"; font-size: 11pt; }a:link { color: rgb(0, 0, 255); }In this book, new methodologies to investigate systems showingchaotic intermittency phenomenon are presented. A new generalmethodology to evaluate the reinjection probability density function(RPD) is developed in Chapters VI to IX. The key of this formulationis the introduction of a new function, called M(x), which is utilizedto calculate the RPD function in place to consider the huge number ofnumerical or experimental data. The function M(x) depends on twointegrals, this characteristic reduces the influence on thestatistical fluctuations in the data series. Also, the function M(x)is easy to evaluate from the data series. This methodology isextended to evaluate the noisy reinjection probability density(NRPD), the noisy probability of the laminar length and the noisycharacteristic relation. In Chapter X, wepresent a new theoretical approach toobtain the RPD directly from the analytical expression of the map.Estimated RPD enables analytic evaluation of the characteristicexponent traditionally used to characterize the intermittency type.The proposed theoretical method is general and very simple to use.Finally in Chapter XI, a new scheme to evaluate the RPD functionusing the Perron-Frobenius operator is developed. On the other hand,the analytical RPD functions, obtained with these threemethodologies, are more general than the previous ones; and theclassical uniform reinjection is only a particular case. The RPDfunctions and other statistical variables of intermittency,calculated using the three new methodologies, are compared withnumerical computations showing very good agreement.