{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:40:46Z","timestamp":1774312846811,"version":"3.50.1"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>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: chaos<jats:sub>1<\/jats:sub>+ chaos<jats:sub>2<\/jats:sub>+ \u22ef + chaos<jats:sub>N<\/jats:sub>= order, where chaos<jats:sub>i<\/jats:sub>, i = 1, 2, \u2026, 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.<\/jats:p>","DOI":"10.1142\/s0218127414500084","type":"journal-article","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T06:27:33Z","timestamp":1392877653000},"page":"1450008","source":"Crossref","is-referenced-by-count":38,"title":["Generalized Form of Parrondo's Paradoxical Game with Applications to Chaos Control"],"prefix":"10.1142","volume":"24","author":[{"given":"Marius-F.","family":"Danca","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Avram Iancu University, 400380 Cluj-Napoca, Romania"},{"name":"Romanian Institute for Science and Technology, 400487 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Fe\u010dkan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynsk\u00e1 dolina, 842 48 Bratislava, Slovakia"},{"name":"Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Romera","sequence":"additional","affiliation":[{"name":"Instituto de Tecnologias Fisicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cientificas (CSIC), Serrano 144, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,2,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219477510000010"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.10.003"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2004.1283"},{"key":"rf4","volume-title":"Theory of Games and Statistical Decisions","author":"Blackwell D.","year":"1954"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.10000"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023962"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412502586"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0172-6"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.08.019"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/030600436"},{"key":"rf13","volume-title":"An Introduction to Difference Equations","author":"Elaydi S.","year":"2005"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1063\/1.4772966"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1038\/47220"},{"key":"rf16","first-page":"206","volume":"14","author":"Harmer G. 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