Analytical evaluation of the reinjection probability density function in chaotic intermittency

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