Effect of Noise on Nonhyperbolic Chaotic Attractors

Journal Article · Sat Aug 01 00:00:00 EDT 1998 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.81.1397· OSTI ID:641546

Schroer, C G ^[1]; Ott, E ^[2]; Yorke, J A ^[3]

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1. Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)
2. Institute for Plasma Research, Department of Electrical Engineering, Department of Physics, and Institute for Systems Research, University of Maryland, College Park, Maryland 20742 (United States)
3. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

We consider the effect of small noise of maximum amplitude {var_epsilon} on a chaotic system whose noiseless trajectories limit on a fractal strange attractor. For the case of nonhyperbolic attractors of two-dimensional maps the effect of noise can be much stronger than for hyperbolic attractors. In particular, the maximum over all noisy orbit points of the distance between the noisy orbit and the noiseless nonhyperbolic attractor scales like {var_epsilon}{sup 1/D{sub 1}} (D{sub 1}{gt}1 is the information dimension of the attractor), rather than like {var_epsilon} (the hyperbolic case). We also find a phase transition in the scaling of the time averaged moments of the deviations of a noisy orbit from the noiseless attractor. {copyright} {ital 1998} {ital The American Physical Society }

• OSTI ID: 641546
• Journal Information: Physical Review Letters, Vol. 81, Issue 7; Other Information: PBD: Aug 1998
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
NOISE
TRAJECTORIES
FRACTALS
ATTRACTORS
SCALING
PHASE TRANSFORMATIONS