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|Title: ||Noisy one-dimensional maps near a crisis .1. Weak Gaussian white and colored noise|
|Authors: ||REIMANN, Peter|
|Issue Date: ||1996|
|Publisher: ||PLENUM PUBL CORP|
|Citation: ||JOURNAL OF STATISTICAL PHYSICS, 82(5-6). p. 1467-1501|
|Abstract: ||We study one-dimensional single-humped maps near the boundary crisis at fully developed chaos in the presence of additive weak Gaussian white noise. By means of a new perturbation-like method the quasi-invariant density is calculated from the invariant density at the crisis in the absence of noise. In the precritical regime, where the deterministic map may show periodic windows, a necessary and sufficient condition for the validity of this method is derived. From the quasi-invariant density we determine the escape rate, which has the form of a scaling law and compares excellently with results from numerical simulations. We find that deterministic transient chaos is stabilized by weak noise whenever the maximum of the map is of order z > 1. Finally, we extend our method to more general maps near a boundary crisis and to multiplicative as well as colored weak Gaussian noise. Within this extended class of noises and for single-humped maps with any fixed order z > 0 of the maximum, in the scaling law for the escape rate both the critical exponents and the scaling function are universal.|
|Notes: ||Reimann, P, LIMBURGS UNIV CENTRUM,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.|
|ISI #: ||A1996TW33000011|
|Type: ||Journal Contribution|
|Appears in Collections: ||Research publications|
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