Affordable Access

deepdyve-link deepdyve-link
Publisher Website

Logarithmic periodicities in the bifurcations of type-I intermittent chaos

Authors
Type
Preprint
Publication Date
Submission Date
Identifiers
DOI: 10.1103/PhysRevLett.92.254102
arXiv ID: nlin/0405047
Source
arXiv
License
Unknown
External links

Abstract

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.

Statistics

Seen <100 times