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dc.contributor.authorGuillamon Grabolosa, Antoni
dc.contributor.authorFontich, Ernest
dc.contributor.authorSardañés, Josep
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2016-02-18T12:16:37Z
dc.date.available2016-02-18T12:16:37Z
dc.date.issued2015-12-21
dc.identifier.citationGuillamon, A., Fontich, E., Sardañés, J. Bifurcations analysis of oscillating hypercycles. "Journal of theoretical biology", 21 Desembre 2015, vol. 387, p. 23-30.
dc.identifier.issn0022-5193
dc.identifier.urihttp://hdl.handle.net/2117/83104
dc.description.abstractWe investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n > 4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium points collide (named Q(SS)). It has also been reported that, for values below Q(SS), the system goes to extinction. In this paper, we use a suitable Poincare map associated to the hypercycle system to analyze the dynamics in the bistability regime, where both oscillatory dynamics and extinction are possible. The stable periodic orbit is identified, together with an unstable periodic orbit. In particular, we are able to unveil the vanishing mechanism of the oscillatory dynamics: a saddle-node bifurcation of periodic orbits as the replication quality factor, Q, undergoes a critical fidelity threshold, O-PO. The identified bifurcation involves the asymptotic extinction of all hypercycle members, since the attractor placed at the origin becomes globally stable for values Q < Q(PO). Near the bifurcation, these extinction dynamics display a periodic remnant that provides the system with an oscillating delayed transition. Surprisingly, we found that the value of Q(PO) is slightly higher than Q(SS), thus identifying a gap in the parameter space where the oscillatory dynamics has vanished while the unstable equilibrium points are still present. We also identified a degenerate bifurcation of the unstable periodic orbits for Q=1. (C) 2015 Elsevier Ltd. All rights reserved.
dc.format.extent8 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
dc.subject.lcshBifurcation theory
dc.subject.otherApplied mathematics
dc.subject.otherBifurcations
dc.subject.otherHypercycles
dc.subject.otherOrigins of life
dc.subject.otherPrebiotic evolution
dc.subject.otherSelf-replication
dc.subject.otherGhosts
dc.subject.otherTransitions
dc.subject.otherEvolution
dc.subject.otherModel
dc.titleBifurcations analysis of oscillating hypercycles
dc.typeArticle
dc.subject.lemacBifurcació, Teoria de la
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.1016/j.jtbi.2015.09.018
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
local.identifier.drac17511557
dc.description.versionPostprint (published version)
local.citation.authorGuillamon, A.; Fontich, E.; Sardañés, J.
local.citation.publicationNameJournal of theoretical biology
local.citation.volume387
local.citation.startingPage23
local.citation.endingPage30


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