Singularities in the fluctuation of on-off intermittency

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Statistical Physics

Background:

• On-off intermittency is a phenomenon characterized by intermittent bursts of activity.
• Understanding the scaling properties of fluctuations is crucial for characterizing chaotic systems.
• Large deviation theory provides a framework for analyzing rare events in stochastic processes.

Purpose of the Study:

• To investigate the scaling properties of fluctuations, specifically the large deviation property, in a two-dimensional piecewise linear map exhibiting on-off intermittency.
• To identify and characterize the different fluctuation phases and their transitions.
• To examine how these properties change at the onset of on-off intermittency.

Main Methods:

• Analysis of a two-dimensional piecewise linear map model.
• Application of large deviation theory to study fluctuation scaling.
• Investigation of q-weighted averages to detect singularities.
• Examination of the coupled logistic map as a related system.

Main Results:

• Identification of three distinct phases of fluctuation.
• Discovery of singularities (jumps or plateaus) in q-weighted averages due to phase transitions.
• Observation that at the onset of on-off intermittency, one phase disappears, weakening the singularity but increasing its probability.
• Singularity analysis on the coupled logistic map confirms these findings.

Conclusions:

• The fluctuation scaling in on-off intermittency exhibits distinct phase transitions with observable singularities.
• The onset of on-off intermittency leads to a modification of these singularities, making them less pronounced but more frequent.
• The findings provide insights into the statistical behavior of chaotic systems near intermittency transitions.