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Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors

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Kantz,  H.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Grebogi,  C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Prasad,  A.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Sinde,  E.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Kantz, H., Grebogi, C., Prasad, A., Lai, Y. C., & Sinde, E. (2002). Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors. Physical Review E, 65(2): 026209. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000065000002026209000001&idtype=cvips&gifs=yes.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-3822-A
Abstract
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.