Type-II intermittency characteristics in the presence of noise

TL;DR

This paper analytically investigates the distribution of laminar phases in type-II intermittency influenced by noise, revealing that the mean laminar phase length's dependence on criticality is robust across different reinjection probabilities.

Contribution

It derives the law for laminar phase distribution in noisy type-II intermittency and shows the mean phase length dependence is independent of reinjection probability assumptions.

Findings

Derived the distribution law for laminar phases.

Confirmed the mean phase length dependence is robust.

Validated the results across different reinjection probabilities.

Abstract

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar phases, which has never been obtained hitherto. The already known dependence of the mean length of the laminar phases on the criticality parameter [PRE 68 (2003) 036203] follows as a corollary of the carried out research. We also prove that this dependence obtained earlier under the assumption of the fixed form of the reinjection probability does not depend on the relaminarization properties, and, correspondingly, the obtained expression of the mean length of the laminar phases on the criticality parameter remains correct for different types of the reinjection probability.