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Scaling law in Saddle-node bifurcations for one-dimensional maps: a complex variable approach

dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorMartins, Nuno
dc.contributor.authorSardanyés, Josep
dc.date.accessioned2015-09-10T09:54:23Z
dc.date.available2015-09-10T09:54:23Z
dc.date.issued2012-01
dc.description.abstractThe study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.por
dc.identifier.citationDUARTE, J.; [et al] – Scaling law in Saddle-node bifurcations for one-dimensional maps: a complex variable approach. Nonlinear Dynamics. ISSN: 0924-090X. Vol. 67, nr. 1 (2012), pp. 541-547por
dc.identifier.issn0924-090X
dc.identifier.urihttp://hdl.handle.net/10400.21/5137
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherSpringerpor
dc.relationFundação para a Ciência e a Tecnologia - Program POCI 2010/FEDER
dc.relationHuman Frontier Science Program Organization - Grant RGP12/2008 (JS)
dc.subjectScaling Lawpor
dc.subjectSaddle-Node Bifurcationspor
dc.subjectOne-Dimensional Mapspor
dc.subjectComplex Variablepor
dc.subjectCritical slowing-down
dc.subjectIntermittency
dc.subjectCooperation
dc.subjectTransitions
dc.subjectHypercycles
dc.subjectExtinctions
dc.subjectModels
dc.subjectGhosts
dc.titleScaling law in Saddle-node bifurcations for one-dimensional maps: a complex variable approachpor
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage547por
oaire.citation.issue1por
oaire.citation.startPage541por
oaire.citation.titleNonlinear Dynamicspor
oaire.citation.volume67por
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.latestForDiscovery4dbec82a-caa4-4662-b156-af73687e867f

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