In-out intermittency in partial differential equation and ordinary differential equation models

Area of Science:

• Dynamical Systems
• Astrophysics
• Plasma Physics

Background:

• Dynamical systems exhibiting intermittency are crucial for understanding complex phenomena.
• Mean-field dynamo models are widely used to study stellar magnetic variability.
• Invariant submanifolds play a key role in the behavior of dynamical systems.

Purpose of the Study:

• To provide concrete evidence for in-out intermittency in partial differential equation (PDE) and ordinary differential equation (ODE) models of mean-field dynamos.
• To differentiate in-out intermittency from on-off intermittency based on system structure.
• To explore the physical relevance of in-out intermittency in various dynamical settings.

Main Methods:

• Analysis of partial differential equation (PDE) and ordinary differential equation (ODE) models.
• Investigation of systems with invariant submanifolds.
• Examination of the absence of skew product structure in dynamical systems.

Main Results:

• Demonstration of in-out intermittency in axisymmetric mean-field dynamo models.
• Confirmation that in-out intermittency requires an absence of skew product structure.
• Identification of dynamics where transverse dynamics alter tangential dynamics away from the invariant manifold.

Conclusions:

• In-out intermittency is a significant dynamical behavior with potential physical relevance.
• The findings contribute to understanding the large-scale magnetic variability observed in the Sun and solar-type stars.
• This study highlights the importance of system structure in the manifestation of intermittency.