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Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

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dc.contributor.authorRocha, J. Leonel
dc.contributor.authorTaha, Abdel Kaddous
dc.contributor.authorFournier-Prunaret, Danièle
dc.date.accessioned2016-05-10T14:17:06Z
dc.date.available2016-05-10T14:17:06Z
dc.date.issued2015
dc.description.abstractIn this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.pt_PT
dc.identifier.citationROCHA, J. Leonel; TAHA, Abdel Kaddous; FOURNIER-PRUNARET, Danièle Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models. Applied Mathematics and Information Sciences. ISSN. 1935-0090. Vol. 9 Nr. 5, (2015), 2377-2388.pt_PT
dc.identifier.doi10.12785/amis/090520pt_PT
dc.identifier.issn1935-0090
dc.identifier.urihttp://hdl.handle.net/10400.21/6180
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherNatural Sciences Publishing Copt_PT
dc.subjectBig bang bifurcationpt_PT
dc.subjectFold and flip bifurcation curvespt_PT
dc.subjectKneading sequencespt_PT
dc.subjectSymbolic dynamicspt_PT
dc.subjectWeibull-Gompertz-Fréchet's growth modelspt_PT
dc.titleSymbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth modelspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage2388pt_PT
oaire.citation.issue5pt_PT
oaire.citation.startPage2377pt_PT
oaire.citation.volume9pt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT

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