Type-I Intermittency With Noise Versus Eyelet Intermittency

TL;DR

This paper demonstrates that type-I intermittency with noise and eyelet intermittency are fundamentally the same phenomenon observed under different conditions, confirmed across various dynamical systems.

Contribution

It establishes the equivalence of two previously considered distinct intermittent behaviors through analysis of multiple sample systems.

Findings

Type-I intermittency with noise and eyelet intermittency are equivalent phenomena.

Confirmed the equivalence across quadratic map, Van der Pol oscillator, and Rossler system.

Validated the findings by analyzing the upper boundary of intermittent behavior.

Abstract

In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rossler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization.