Intermittency Reinjection Probability Function with and without Noise Effects

摘要

Intermittency is an occurrence of a signal that alternates chaotic burst between quasi-regular periods called laminar phases. It has been studied that number of chaotic burst increases with an external parameter, then intermittency phenomenon is a continuous route from regular to chaotic motions. There are several topics in physics, biology and economy where the intermittency phenomenon appears. The correct evaluation of the intermittency phenomenon contributes to a better prediction and a proper description of these topics. Here is introduced a new technique to obtain the reinjection probability function for type I, II and III intermittency. The new reinjection probability function is more general and it includes the constant reinjection probability function as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined considering with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy reinjection probability density is developed, which basically consists in extending the procedure used to derive the noiseless reinjection probability density. The analytical results show a good agreement with numerical simulations and for large values of the instability parameter, the characteristic relations approach the associated ones to the noiseless intermittency; however, for low values of the instability parameter, the characteristic relations reach a saturation level depending on the noise reinjection function.