On-off intermittency over an extended range of control parameter

Area of Science:

• Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• On-off intermittency is a phenomenon characterized by intermittent bursts of activity separated by quiescent periods.
• Standard on-off intermittency is typically observed at a specific critical point of a control parameter.
• The distribution of quiescent periods in standard on-off intermittency follows a power-law with a characteristic exponent.

Purpose of the Study:

• To propose a novel phenomenological model that exhibits on-off intermittency.
• To investigate the behavior of on-off intermittency over an extended range of a control parameter.
• To analyze the statistical properties of the quiescent periods in the proposed model.

Main Methods:

• Development of a simple phenomenological model.
• Numerical simulations to explore the model's dynamics.
• Statistical analysis of the distribution of 'off' periods.

Main Results:

• The model exhibits on-off intermittency over an extended range of the control parameter.
• The distribution of 'off' periods displays a power-law tail.
• The exponent of this power-law tail varies continuously between -1 and -2.
• This behavior deviates from the standard exponent of -3/2 observed in typical on-off intermittency.

Conclusions:

• The proposed model provides a new framework for understanding on-off intermittency.
• The observed continuous variation in the exponent suggests a richer class of intermittency than previously recognized.
• The interplay between dynamics slowing down and a systematic drift drives this nontrivial behavior.