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Strong and weak Allee effects and chaotic dynamics in Richards' growths

2013-11Journal article Open access
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dc.contributor.authorRocha, J. Leonel
dc.contributor.authorFournier-Prunaret, Danièle
dc.contributor.authorTaha, Abdel-Kaddous
dc.date.accessioned2013-11-07T18:24:36Z
dc.date.available2013-11-07T18:24:36Z
dc.date.issued2013-11
dc.description.abstractIn this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.por
dc.identifier.citationROCHA, J. Leonel; FOURNIER-PRUNARET, Danièle; TAHA, Abdel-Kaddous - Strong and weak Allee effects and chaotic dynamics in Richards' growths. Discrete and Continuous Dynamical Systems-Series B. ISSN 1531-3492. Vol. 18, nr. 9 (2013), p. 2397-2425por
dc.identifier.issn1531-3492
dc.identifier.other10.3934/dcdsb.2013.18.2397
dc.identifier.urihttp://hdl.handle.net/10400.21/2883
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherAmer Inst Mathematical Sciencespor
dc.relationCEAUL
dc.relationStrategic Project - UI 6 - 2011-2012
dc.subjectPopulation dynamicspor
dc.subjectStrong and weak Allee effectspor
dc.subjectRichards' equationpor
dc.subjectFold and flip bifurcationspor
dc.subjectSymbolic dynamicspor
dc.subjectModelspor
dc.subjectExtinctionpor
dc.subjectMetapopulationpor
dc.subjectBifurcationpor
dc.subjectDensitiespor
dc.titleStrong and weak Allee effects and chaotic dynamics in Richards' growthspor
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleStrategic Project - UI 6 - 2011-2012
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/PEst-OE%2FMAT%2FUI0006%2F2011/PT
oaire.citation.conferencePlaceSpringfieldpor
oaire.citation.endPage2425por
oaire.citation.issue9por
oaire.citation.startPage2397por
oaire.citation.titleDiscrete and Continuous Dynamical Systems-Series Bpor
oaire.citation.volume18por
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccesspor
rcaap.typearticlepor
relation.isProjectOfPublication4049804e-6284-4ac0-95b3-63a7ae59e09d
relation.isProjectOfPublication.latestForDiscovery4049804e-6284-4ac0-95b3-63a7ae59e09d

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