Reinjection probability density in type-III intermittency

A method to obtain the reinjection probability density (RPD) for systems showing type-III intermittency phenomenon is presented. The method emerges as a natural extension of a recent procedure we established to derive the RPD for type-II intermittency. A new two-parameter class of reinjection probability densities is presented to describe a broad class of type-III intermittency maps. Our RPD expression also provides information about the lower bound of the reinjection (LBR). The new characteristic relation εβ depends on the LBR and it has a critical exponent β such that −1<β<−0.5. The corresponding analytical duration probability densities are also derived in agreement with the numerical computation. The main classical results can be extracted from our RPD as particular cases.