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Dynamic Parrondo’s paradox

Authors
Journal
Physica D Nonlinear Phenomena
0167-2789
Publisher
Elsevier
Publication Date
Volume
218
Issue
2
Identifiers
DOI: 10.1016/j.physd.2006.05.004
Keywords
  • Chaos
  • One-Dimensional Dynamics
  • Composition Of Maps
  • Turbulence
  • Parrondo’S Paradox
Disciplines
  • Mathematics

Abstract

Abstract This paper is focused on studying Parrondo’s paradox in non-linear dynamics, specifically how the periodic combination of the individual maps f and g can give rise to chaos or order. We construct dynamical systems exhibiting the paradox for several notions of chaos derived from topological dynamics. The effect of altering the order of the combination, i.e. considering f ∘ g or g ∘ f , is analyzed, as well as the robustness of the Parrondo effect under small perturbations. Conditions for avoiding Parrondian dynamics are also obtained, placing special emphasis on the notion of chaos given by turbulence.

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