Limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness

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dc.contributor.authorCetin, Kivanc
dc.contributor.authorAfsar, Ozgur
dc.contributor.authorTirnakli, Ugur
dc.date.accessioned2019-10-27T19:53:49Z
dc.date.available2019-10-27T19:53:49Z
dc.date.issued2015
dc.departmentEge Üniversitesien_US
dc.description.abstractIn this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities. The first one is the well-known white noise, whereas the second is a newly defined one, named as quartic term, which makes contributions from the own structure of the map. As the chaos threshold is approached, the iterates of the standard logistic map (i.e. noise-free) have strong correlations and the standard Central Limit Theorem is not valid anymore. In a recent work (Tirnakli, 2009), it has been shown that the limit distribution seems to converge to q-Gaussian distribution, which maximizes the nonadditive entropy S-q equivalent to (1 -Sigma(i)p(i)(q)) / (q - 1) under appropriate conditions. In this work, we investigate the effect of these contributions (i.e. white noise and quartic term) on the limit distribution and on the range of the obtained q-Gaussian distribution. As a result of these findings, under the existence of white noise and also the quartic term, we analyse the validity of the scaling relations among correlation, fractality, the Lyapunov divergence and q-Gaussian distributions, which have recently been observed in (Afsar, 2014). The results obtained here strengthen the argument that the central limit behaviour is given by a q-Gaussian as the chaos threshold is approached and indicate that the scaling relations, obtained for the standard logistic map, among the range of the q-Gaussian, the correlation dimension, the correlation length, the Lyapunov exponent, fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term. (C) 2014 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipTUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [112T083]; Ege UniversityEge University [2012FEN076]en_US
dc.description.sponsorshipThis work has been supported by TUBITAK (Turkish Agency) under the Research Project number 112T083 and by Ege University under the Research Project number 2012FEN076. U.T. is a member of the Science Academy, Istanbul, Turkey.en_US
dc.identifier.doi10.1016/j.physa.2014.12.029
dc.identifier.endpage282en_US
dc.identifier.issn0378-4371
dc.identifier.issn1873-2119
dc.identifier.issn0378-4371en_US
dc.identifier.issn1873-2119en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage269en_US
dc.identifier.urihttps://doi.org/10.1016/j.physa.2014.12.029
dc.identifier.urihttps://hdl.handle.net/11454/40352
dc.identifier.volume424en_US
dc.identifier.wosWOS:000350192200028en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Bven_US
dc.relation.ispartofPhysica A-Statistical Mechanics and Its Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectChaos thresholden_US
dc.subjectCentral limit behaviouren_US
dc.subjectThe logistic map with noiseen_US
dc.titleLimit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustnessen_US
dc.typeArticleen_US

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