TY - JOUR
T1 - Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors
AU - Kantz, H
AU - Grebogi, C
AU - Prasad, A
AU - Lai, Y-C
AU - Sinde, E
PY - 2002/2
Y1 - 2002/2
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.
U2 - 10.1103/PhysRevE.65.026209
DO - 10.1103/PhysRevE.65.026209
M3 - Article
SN - 1539-3755
VL - 65
JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
IS - 2
M1 - 026209
ER -