Chaotic intermittency as a random telegraphic signal

A wide range of processes can be characterized by a random telegraphic signal, which is essentially a time-dependent signal that oscillates randomly between two distinct values. Meanwhile, the concept of chaotic intermittency holds significant relevance across various fields, including physics, engineering, and medicine, among others. This paper aims to establish a connection between these two topics to deepen our understanding of chaotic intermittency. Specifically, we explore how the probabilities associated with waiting or sojourn times in random telegraphic signals can be linked to the probability density of laminar lengths, as determined through a novel theoretical framework of chaotic intermittency. To validate our theoretical findings, we conduct a series of numerical experiments focused on three different types of intermittencies: type I, type II, and type III. We demonstrate that the correlation between random telegraphic signals and chaotic intermittency offers several advantages. In particular, this formulation enables the evaluation of the probability that the system remains in either a laminar or chaotic phase. Therefore, this technique facilitates the comparison between analytical and numerical approaches, and we conclude that there is a very close alignment between both approaches.