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

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 fielddynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs insystems with invariant submanifolds and, as opposed to on--off intermittencywhich can also occur in skew product systems, it requires an absence of skewproduct structure. By this we mean that the dynamics on the attractorintermittent to the invariant manifold cannot be expressed simply as thedynamics on the invariant subspace forcing the transverse dynamics; thetransverse dynamics will alter that tangential to the invariant subspace whenone is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skewproduct structure, this type of behaviour may be of physical relevance in avariety of dynamical settings. The models employed here to demonstrate in--out intermittency areaxisymmetric mean--field dynamo models which are often used to study theobserved large scale magnetic variability in the Sun and solar-type stars. Theoccurrence of this type of intermittency in such models may be of interest inunderstanding some aspects of such variabilities.