Stochastic to deterministic crossover of fractal dimension for a Langevin equation

Details Stochastic to deterministic crossover of fractal dimension for a Langevin equation Stochastic to deterministic crossover of fractal dimension for a Langevin equation

1993-03-12

arxiv.org/abs/chao-dyn/9303004v1

Nonlinear Sciences

Chaotic Dynamics

12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev. E, April, 1993

Scientific paper

10.1103/PhysRevE.47.3753

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.

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