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 partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field dynamos . This type of intermittency [introduced in P. Ashwin, E. Covas, and R. Tav akol, Nonlinearity 9, 563 (1999)] occurs in systems with invariant submanif olds and, as opposed to on-off intermittency which can also occur in skew p roduct systems, it requires an absence of skew product structure. By this w e mean that the dynamics on the attractor intermittent to the invariant man ifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that ta ngential to the invariant subspace when one is far enough away from the inv ariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behavior may be of phys ical relevance in a variety of dynamical settings. The models employed here to demonstrate in-out intermittency are axisymmetric mean-field dynamo mod els which are often used to study the observed large-scale magnetic variabi lity in the Sun and solar-type stars. The occurrence of this type of interm ittency in such models may be of interest in understanding some aspects of such variabilities. (C) 2001 American Institute of Physics.