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Type: Journal article
Title: Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox
Author: Amengual, P.
Allison, A.
Toral, R.
Abbott, D.
Citation: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004; 460(2048):2269-2284
Publisher: Royal Soc London
Issue Date: 2004
ISSN: 1364-5021
Statement of
P. Amengual, A. Allison, R. Toral and D. Abbott
Abstract: Parrondo’s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker–Planck equation, that rigorously establish the connection between Parrondo’s games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo’s games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.
Description: © 2004 The Royal Society
DOI: 10.1098/rspa.2004.1283
Appears in Collections:Aurora harvest 6
Electrical and Electronic Engineering publications

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