Effect of the lower boundary of reinjection and noise in Type-II intermittency

Abstract

We implement a recent methodology to study type-II intermittency considering different values of the lower boundary of reinjection (LBR) and the noise intensity. With this approach, analytical expressions for the reinjection probability density (RPD) are accurately obtained. The proposed RPD has a piecewise definition addressing the different reinjection mechanisms appearing in the system depending on the LBR value and the noise intensity. Also, the new probability density of the laminar lengths is calculated. When LBR = 0, the noisy probability density of the laminar lengths presents a cutoff, which disappears for noise strength different to zero. The theoretical results are verified with numerical simulations.