INFLUENCE OF NOISE NEAR BLOWOUT BIFURCATION

We consider effects of zero-mean additive noise on systems that an und ergoing supercritical blowout bifurcation, i.e., where a chaotic attra ctor in an invariant subspace loses transverse stability to a nearby o n-off intermittent attractor. We concentrate on the low noise limit an d two statistical properties of the trajectories; the variance of the normal component and the mean first crossing time of the invariant sub space. Before blowout we find that the asymptotic variance scales alge braically with the noise level and exponentially with the Lyapunov exp onent. After blowout it is limited to the nonzero variance of the asso ciated on-off intermittent state. Surprisingly, for a large enough Lya punov exponent, the effect of added noise can be to decrease rather th an increase the variance. The mean crossing time becomes infinite at a nd after the blowout in the limit of small noise; after the blowout th en is exponential dependence on the Lyapunov exponent and algebraic de pendence on the noise level. The results are obtained using a drift-di ffusion model of Venkataramani et al. The results are confirmed in num erical experiments on a smooth mapping. We observe that although there are qualitative similarities between bubbling (noise-driven) and on-o ff intermittency (dynamics-driven), these can be differentiated using the statistical properties of the variance of the normal dynamics and the mean crossing time of the invariant subspace in the limit of low n oise.