Reinjection Probability Function with Lower Bound of the Reinjection for Intermittency Type III

Abstract

Intermittency is characterized by the successive occurrence of a signal that alternates chaotic burst between quasi-regular periods or laminar phases. The intermittency phenomenon is a continuous route from regular to chaotic motions and it is classified into three types in function of the local Poincaré map and the value of the respective Floquet multiplier (local property): type I, type II and type III. To determine the intermittency behavior and characteristic parameters such as the average laminar length it is necessary to know the reinjection probability function or RPF (global property). At the present several books and papers consider that the RPF is constant or some artificial function. However there are some tests in which theses conditions are not satisfy. In this paper is introduced a new methodology to obtain the reinjection probability function for intermittency type III with and without lower bound of the reinjection. This technique permits to reach a more general RPF and it includes the constant RPF as a particular case. The proposed technique to obtain the RPF shows advantages because it reduces the noise in experimental and numerical data. Two maps are analyzed to prove the accuracy of the new RPF function and the viability of the proposed technique to obtain it.