Abstract
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.
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