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- Title
Generalized Form of Parrondo's Paradoxical Game with Applications to Chaos Control.
- Authors
Danca, Marius-F.; Fečkan, Michal; Romera, Miguel
- Abstract
In this paper, we show that a generalized form of Parrondo's paradoxical game can be applied to discrete systems, working out the logistic map as a concrete example, to generate stable orbits. Written in Parrondo's terms, this reads: chaos1 + chaos2 + ⋯ + chaosN = order, where chaosi, i = 1, 2, ..., N, are denoted as the chaotic behaviors generated by N values of the parameter control, and by order one understands some stable behavior. The numerical results are sustained by quantitative dynamics generated by Parrondo's game. The implementation of the generalized Parrondo's game is realized here via the parameter switching (PS) algorithm for continuous-time systems [Danca, 2013] adapted to the logistic map. Some related results for more general maps on averaging, which represent discrete analogies of the PS method for ODE, are also presented and discussed.
- Subjects
GENERALIZATION; GAME theory; CHAOS theory; CONTROL theory (Engineering); DISCRETE systems; LOGISTICS; MATHEMATICAL mappings; SWITCHING theory
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2014, Vol 24, Issue 1, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127414500084