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Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

2016-04Journal article Restricted access
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dc.contributor.authorRocha, J. Leonel
dc.contributor.authorTaha, Abdel-Kaddous
dc.contributor.authorFournier-Prunaret, Danièle
dc.date.accessioned2016-07-04T11:34:29Z
dc.date.available2016-07-04T11:34:29Z
dc.date.issued2016-04
dc.description.abstractThe main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.pt_PT
dc.identifier.citationROCHA, J. Leonel; TAHA, Abdel-Kaddous; FOURNIER-PRUNARET, Danièle - Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects. Nonlinear dynamics. ISSN 0924-090X. Vol. 84, Nr. 2, (2016), 607-626.pt_PT
dc.identifier.doi10.1007/s11071-015-2510-6pt_PT
dc.identifier.issn0924-090X
dc.identifier.issn1573-269X
dc.identifier.urihttp://hdl.handle.net/10400.21/6290
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s11071-015-2510-6pt_PT
dc.subjectVon Bertalanffy's dynamicspt_PT
dc.subjectStrong and weak Allee effectspt_PT
dc.subjectBig bang bifurcationpt_PT
dc.subjectExtinctionpt_PT
dc.titleBig bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effectspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage626pt_PT
oaire.citation.issue2pt_PT
oaire.citation.startPage607pt_PT
oaire.citation.volume84pt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT

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