In--out intermittency in PDE and ODE models

TL;DR

This paper provides evidence of in--out intermittency in PDE and ODE models of mean field dynamos, highlighting its distinct nature from on--off intermittency and its potential relevance to solar magnetic variability.

Contribution

It demonstrates the presence of in--out intermittency in mean field dynamo models, emphasizing its occurrence in systems lacking skew product structure and its possible physical significance.

Findings

In--out intermittency observed in PDE and ODE dynamo models.

This intermittency type differs from on--off intermittency by requiring non-skew product dynamics.

Potential implications for understanding solar magnetic variability.

Abstract

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.