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

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Abstract
We show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise, even when each individ- ual 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 sim- ple two-dimensional switching model and by a simulation of a convectively driven dynamo.