Abstract
We describe one-dimensional discrete difFusive motion that is driven by a purely deterministic system, the logistic map. We find normal diffusive motion above a critical value k, of the chaotic parameter. At A, i, the diftusion constant D plays the role of an order parameter, with a critical exponent of 1/2. In the presence of external noise, D is expressed in terms of a universal scaling function and the critical exponent associated with the noise is found to be 1. We also consider biased di6'usive motion driven by the logistic map. We find that the di8'usion process thus generated is di6'erent from biased di6'usion. In contrast to the case of the biased random walker where all configurations (walks ) are still possible, here certain configurations are not allowed. However, the statistical properties approach those for biased di6'usion in the infinite time limit. We define a measure of the e6'ective randomness.
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