The Perron-Frobenius operator to calculate the reinjection probability density function in chaotic intermittency

DEL RIO, EZEQUIEL; ELASKAR, SERGIO

Madrid

Congreso; 15th Experimental Chaos and Complexity Conference; 2018

Universidad Rey Juan Carlos

p { margin-bottom: 0.25cm; direction: ltr; color: rgb(0, 0, 0); line-height: 120%; }p.western { font-family: "Liberation Serif","Times New Roman",serif; font-size: 12pt; }p.cjk { font-family: "WenQuanYi Micro Hei"; font-size: 12pt; }p.ctl { font-family: "Lohit Devanagari"; font-size: 12pt; }In several experiments theobtained data show intermittency. Therefore, to describe correctlythe phenomenon it is necessary to evaluate the statistical propertiesof intermittency. Here, the Perron-Frobenius operator is applied tostudy the reinjection process in chaotic intermittency [1]. By meanof this operator, the theoretical expressions for the reinjectionprobability density function and the probability density of thelaminar lengths for several maps can be obtained [2]. To validate thenew expressions, the analytical functions are compared with numericaldata. A high accuracy between theoretical equations and numericalsimulations was found. Also, comparisons between the new expressionswith those obtained using the M(x) function methodology are carriedout [3,4]. The results show that the RPD can acquire a richer andbroader behavior than those given by the classical theory. Finally,the advantages and difficulties of both methodologies are described.References1 - S. Elaskar, E. del Río, E.Zapico, Nonlinear Dynamics, 86, 1107-1116 (2016).2 - S. Elaskar, E. del Río,New Advances on Chaotic Intermittency and Applications. Springer, NewYork (2017).3 - E. del Rio, S. Elaskar,Int. J. of Bifurcation and Chaos, 20, 1185-1191 (2010)4 - S. Elaskar, E. del Río, J.Donoso, Physica A, 390, 2759-2768 (2011)