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REVISITING PARRONDO'S PARADOX FOR THE LOGISTIC FAMILY

The aim of this paper is to investigate the existence of Parrondo's paradox for the logistic family fa(x) = ax(1 - x), x ∈ [0, 1], when the parameter value a ranges over the interval [1, 4]. We find that a paradox of type "order + order = chaos" arises for both physically observable and topological chaos, while a "chaos + chaos = order" paradox can be only detected for the case of physically observable chaos. In addition, we raise the question of whether the paradox "chaos + chaos = order" can appear in the topological sense or whether, as our computations seem to show, it is impossible for the logistic family.