The lengths distribution of laminar phases for type-I intermittency in the presence of noise

TL;DR

This paper analyzes how noise influences the distribution of laminar phase lengths in type-I intermittency, providing analytical laws and confirming them through experiments and simulations.

Contribution

It develops an analytical theory for laminar phase length distribution in noisy type-I intermittency, extending previous results and validating them with experimental and numerical data.

Findings

Analytical laws for laminar phase length distribution in noisy systems.

Good agreement between theory, experiments, and simulations.

Insights into physical scenarios where this mechanism applies.

Abstract

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [PRE 62 (2000) 6304] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.