Destabilization by noise of tranverse perturbations to heteroclinic cycles: a simple model and an example from dynamo theory

We show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise, even when each individual fixed point of the cycle is stable to transverse modes. A condition that favours this process is that the linearization of the dynamics in the transverse direction be characterized by a non-normal matrix. The phenomenon is illustrated by a simple two-dimensional switching model and by a simulation of a convectively driven dynamo.