Logarithmic periodicities in the bifurcations of type-I intermittent chaos

Details Logarithmic periodicities in the bifurcations of type-I intermittent chaos Logarithmic periodicities in the bifurcations of type-I intermittent chaos

2004-05-19

arxiv.org/abs/nlin/0405047v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 6 figures, accepted for publication in PRL (2004)

Scientific paper

10.1103/PhysRevLett.92.254102

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.

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