Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2004-03-12
Nonlinear Sciences
Chaotic Dynamics
Phys. Rev. Lett., to be published; first version of reply rejected
Scientific paper
Lai {\it et al.} \cite{Lai:2002} investigate systems with a stable periodic orbit and a coexisting chaotic saddle. They claim that, by adding white Gaussian noise (GN), averages change with an algebraic scaling law above a certain noise threshold and argue that this leads to a breakdown of shadowability of averages. Here, we show that (i) shadowability is not well defined and even if it were, no breakdown occurs. We clarify misconceptions on (ii) thresholds for GN. We further point out (iii) misconceptions on the effect of noise on averages. Finally, we show that (iv) the lack of a proper threshold can lead to any (meaningless) scaling exponent.
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