TY - JOUR
T1 - Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors
AU - Kantz, Holger
AU - Grebogi, Celso
AU - Prasad, Awadhesh
AU - Lai, Ying-Cheng
AU - Sinde, Erik
PY - 2002
Y1 - 2002
N2 - Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic attractors. Whereas in the presence of tangencies, interactive noise yields attractor deformations, attractors with only dimension variability are robust, despite the fact that shadowing is grossly violated.
AB - Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic attractors. Whereas in the presence of tangencies, interactive noise yields attractor deformations, attractors with only dimension variability are robust, despite the fact that shadowing is grossly violated.
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U2 - 10.1103/PhysRevE.65.026209
DO - 10.1103/PhysRevE.65.026209
M3 - Article
AN - SCOPUS:41349092465
SN - 1063-651X
VL - 65
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 -