Laminar length and characteristic relation in Type-I intermittency

A method to investigate systems showing Type-I intermittency phenomenon is presented. This method is an extension of the procedure we have recently established to study the Type-II and Type-III intermittencies. With this approach, new accurate analytical expressions for the reinjection and the laminar phase length probability densities are obtained. The new theoretical formulas are tested by numerical computation, showing an excellent agreement between analytical models and numerical results. In addition, our method fully generalizes the well-known classical characteristic relations, in such a way that it properly characterizes those systems showing Type-I intermittency.