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Stochastic to deterministic crossover of fractal dimension for a Langevin equation

David A. Egolf·Henry S. Greenside
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Abstract

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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David A. Egolf, Henry S. Greenside. 1993-03-12. Stochastic to deterministic crossover of fractal dimension for a Langevin equation. https://doi.org/10.1103/physreve.47.3753

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