Analytical evaluation of the reinjection probability density function in chaotic intermittency

ELASKAR, SERGIO; DEL RIO, EZEQUIEL; GUTIÉRREZ MARCANTONI, L. F.

Resistencia

Congreso; 2020 IEEE Congreso Bienal de Argentina, ARGENCON 2020 - 2020 IEEE Biennial Congress of Argentina, ARGENCON 2020; 2020

IEEE

The classical theory of intermittency uses the as-sumption that the reinjection probability density function (RPD)is uniform. Nevertheless, more recent studies have developedthe M function methodology which introduced a more generalRPD. Here, we present an analytical approximation to estimatenon-uniform RPD functions. The proposed theoretical method isgeneral and very direct to use. The analytical approximationshows as the RPD depends on the type of pre-reinjectionpoints, extreme or infinite derivative points. For type I and IIintermittency with logarithmic and trigonometric non-linearity,the theoretical predictions are compared with numerical resultsshowing excellent agreement.