Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3464
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
Source: 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.
Keywords: noisy map; crisis; escape rate; scaling and universality; invariant density; transient chaos; colored noise
Document URI: http://hdl.handle.net/1942/3464
DOI: 10.1007/BF02183392
ISI #: A1996TW33000011
Type: Journal Contribution
Appears in Collections:Research publications

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