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The properties of a simple one-dimensional iterated map in the presence of noise are examined. It is demonstrated that there are three distinct classes of noise that generate three 'phases' of the iterated function. Each phase shows universal properties that are independent of the specific form of noise, if this noise is chosen form a given class. The physical interpretation of the model in terms of aggregation is discussed.
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J. M. Deutsch (1985) studied this question.
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