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On chaos, transient chaos and ghosts in single populations models with allee effects

2012-08Journal article Restricted access
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dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorMartins, Nuno
dc.contributor.authorSardanyés, Josep
dc.date.accessioned2015-09-10T09:49:35Z
dc.date.available2015-09-10T09:49:35Z
dc.date.issued2012-08
dc.description.abstractDensity-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.por
dc.identifier.citationDUARTE, J.; JANUÁRIO, C.; MARTINS, N.; SARDANYES, J. – On chaos, transiente chaos and ghosts in single populations models with allee effects. Nonlinear Analysis-Real World Applications. ISSN: 1468-1218. Vol. 13, nr. 4 (2012), pp. 1674-1661.por
dc.identifier.doi10.1016/j.nonrwa.2011.11.022
dc.identifier.issn1468-1218
dc.identifier.urihttp://hdl.handle.net/10400.21/5135
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherPergamon-Elsevierpor
dc.relationFundação para a Ciência e a Tecnologia - Program POCI 2010/FEDER
dc.relationHuman Frontier Science Program Organization - Grant RGP12/2008
dc.relationNational ScienceFoundation - Grant No. NSF PHY05-51164
dc.subjectAllee Effectspor
dc.subjectChaospor
dc.subjectExtinction Transientspor
dc.subjectScaling Lawspor
dc.subjectSingle Species Dynamicspor
dc.subjectTheoretical Ecologypor
dc.subjectTopological Entropypor
dc.titleOn chaos, transient chaos and ghosts in single populations models with allee effectspor
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage1661por
oaire.citation.issue4por
oaire.citation.startPage1647por
oaire.citation.titleNonlinear Analysis-Real World Applicationspor
oaire.citation.volume13por
person.familyNameDuarte
person.familyNameJanuário
person.givenNameJorge
person.givenNameCristina
person.identifier.ciencia-idBC1D-1E83-E2B2
person.identifier.orcid0000-0003-2641-3199
person.identifier.orcid0000-0002-6978-876X
person.identifier.ridG-7261-2011
person.identifier.scopus-author-id35310049800
person.identifier.scopus-author-id56526791400
rcaap.rightsclosedAccesspor
rcaap.typearticlepor
relation.isAuthorOfPublication4dbec82a-caa4-4662-b156-af73687e867f
relation.isAuthorOfPublication42a4023b-b4c4-4456-aaba-d97bf8c14d6a
relation.isAuthorOfPublication.latestForDiscovery42a4023b-b4c4-4456-aaba-d97bf8c14d6a

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