ISSN:
1572-9613
Keywords:
Noisy map
;
crisis
;
escape rate
;
scaling and universality
;
invariant density
;
transient chaos
;
colored noise
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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 orderz〉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 orderz〉0 of the maximum, in the scaling law for the escape rate both the critical exponents and the scaling function are universal.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02183392
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