TY - JOUR

T1 - Influence of noise near blowout bifurcation

AU - Ashwin, Peter

AU - Stone, Emily

PY - 1997

Y1 - 1997

N2 - We consider effects of zero-mean additive noise on systems that are undergoing supercritical blowout bifurcation, i.e., where a chaotic attractor in an invariant subspace loses transverse stability to a nearby on-off intermittent attractor. We concentrate on the low noise limit and two statistical properties of the trajectories; the variance of the normal component and the mean first crossing time of the invariant subspace. Before blowout we find that the asymptotic variance scales algebraically with the noise level and exponentially with the Lyapunov exponent. After blowout it is limited to the nonzero variance of the associated on-off intermittent state. Surprisingly, for a large enough Lyapunov exponent, the effect of added noise can be to decrease rather than increase the variance. The mean crossing time becomes infinite at and after the blowout in the limit of small noise; after the blowout there is exponential dependence on the Lyapunov exponent and algebraic dependence on the noise level. The results are obtained using a drift-diffusion model of Venkataramani et al. The results are confirmed in numerical experiments on a smooth mapping. We observe that although there are qualitative similarities between bubbling (noise-driven) and on-off 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 noise.

AB - We consider effects of zero-mean additive noise on systems that are undergoing supercritical blowout bifurcation, i.e., where a chaotic attractor in an invariant subspace loses transverse stability to a nearby on-off intermittent attractor. We concentrate on the low noise limit and two statistical properties of the trajectories; the variance of the normal component and the mean first crossing time of the invariant subspace. Before blowout we find that the asymptotic variance scales algebraically with the noise level and exponentially with the Lyapunov exponent. After blowout it is limited to the nonzero variance of the associated on-off intermittent state. Surprisingly, for a large enough Lyapunov exponent, the effect of added noise can be to decrease rather than increase the variance. The mean crossing time becomes infinite at and after the blowout in the limit of small noise; after the blowout there is exponential dependence on the Lyapunov exponent and algebraic dependence on the noise level. The results are obtained using a drift-diffusion model of Venkataramani et al. The results are confirmed in numerical experiments on a smooth mapping. We observe that although there are qualitative similarities between bubbling (noise-driven) and on-off 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 noise.

UR - http://www.scopus.com/inward/record.url?scp=0000103165&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.56.1635

DO - 10.1103/PhysRevE.56.1635

M3 - Article

AN - SCOPUS:0000103165

SN - 1063-651X

VL - 56

SP - 1635

EP - 1641

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 2

ER -