New Formulation of the Chaotic Intermittency

Abstract

As we have seen in the previous chapters, in the classical theory of intermittency the uniform density of points reinjected from the chaotic to laminar region is a usual hypothesis. In this chapter we reported on how the reinjection probability density (RPD) can be generalized. Estimation of the universal RPD is based on fitting a linear function to experimental data and it does not require a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets. Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Also an analytical method providing the RPD is explained. It is based on the number of null derivatives of the map at the extreme point. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. The new characteristic exponent is developed, that now is not a single number but is a function depending on the whole map, not on the only the local region. In conclusion, a generalization of the classical intermittency theory is present.