Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection
American Institute of Physics (AIP)
We investigate the robust heteroclinic dynamics arising in a system of ordinary differential equations in R4 with symmetry D4⋉(Z2)2. This system arises from the normal form reduction of a 1:2√ mode interaction for Boussinesq convection. We investigate the structure of a particular robust heteroclinic attractor with “depth two connections” from equilibria to subcycles as well as connections between equilibria. The “subcycle” is not asymptotically stable, due to nearby trajectories undertaking an “excursion,” but it is a Milnor attractor, meaning that a positive measure set of nearby initial conditions converges to the subcycle. We investigate the dynamics in the presence of noise and find a number of interesting properties. We confirm that typical trajectories wind around the subcycle with very occasional excursions near a depth two connection. The frequency of excursions depends on noise intensity in a subtle manner; in particular, for anisotropic noise, the depth two connection may be visited much more often than for isotropic noise, and more generally the long term statistics of the system depends not only on the noise strength but also on the anisotropy of the noise. Similar properties are confirmed in simulations of Boussinesq convection for parameters giving an attractor with depth two connections.
Agence Nationale de la Recherche, France
Russian Foundation for Basic Research
Copyright © 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Chaos Volume 20 (2), article 023133, and may be found at http://dx.doi.org/10.1063/1.3439320
Vol. 20 (2), article 023133
Place of publication