CYCLING CHAOS - ITS CREATION, PERSISTENCE AND LOSS OF STABILITY IN A MODEL OF NONLINEAR MAGNETOCONVECTION

We examine a model system where attractors may consist of a heteroclin ic cycle between chaotic sets; this 'cycling chaos' manifests itself a s trajectories that spend increasingly long periods lingering near cha otic invariant sets interspersed with short transitions between neighb ourhoods of these sets. Such behaviour is robust to perturbations that preserve the symmetry of the system; we examine bifurcations of this state. We discuss a scenario where an attracting cycling chaotic state is created at a blowout bifurcation of a chaotic attractor in an inva riant subspace. This differs from the standard scenario for the blowou t bifurcation in that in our case, the blowout is neither subcritical nor supercritical. The robust cycling chaotic state can be followed to a point where it loses stability at a resonance bifurcation and creat es a series of large period attractors. The model we consider is a nin th-order truncated ordinary differential equation (ODE) model of three -dimensional incompressible convection in a plane layer of conducting fluid subjected to a vertical magnetic field and a vertical temperatur e gradient. Symmetries of the model lead to the existence of invariant subspaces for the dynamics; in particular there are invariant subspac es that correspond to regimes of two-dimensional flows, with variation in the vertical but only one of the two horizontal directions. Stable two-dimensional chaotic flow can go unstable to three-dimensional flo w via the cross-roll instability. We show how the bifurcations mention ed above can be located by examination of various transverse Liapunov exponents. We also consider a reduction of the ODE to a map and demons trate that the same behaviour can be found in the corresponding map. T his allows us to describe and predict a number of observed transitions in these models. The dynamics we describe is new but nonetheless robu st, and so should occur in other applications. (C) 1998 Elsevier Scien ce B.V.