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dc.contributorGuillamon Grabolosa, Antoni
dc.contributorFontich, Ernest
dc.contributorSardanyés, Josep
dc.contributor.authorFarré Puiggalí, Gerard
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractThe symmetric hypercycle with error tail has been widely studied both numerically and analytically in the last years, but there are still many open questions. In this work we will try to give an answer for a few of these questions. Namely we reproduce in higher dimensions a study of the possible coincidence of saddle-node bifurcations for equilibrium points and periodic orbits already done for n=5, we finish the classification of the stability of equilibrium points in any dimension (the case n=4 was still not classified as far as we know) and we try to give a more clear idea of the behaviour of the system in low dimensions (n=2 and n=3). We also reproduce other important results concerning important properties of the hypercycle and give the necessary background in dynamical systems to understand these results. Finally we contrast the ODE model with a completely different approach to model hypercycles which consists in using cellular automata.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherEquilibrium point
dc.subject.otherPeriodic orbit
dc.subject.otherPoincaré map
dc.subject.otherLyapunov stability
dc.subject.otherSaddle-node bifurcation
dc.subject.otherInvariant manifold
dc.subject.otherCellular automata
dc.titleDynamics and transitions in symmetric hypercycles: the role of the hypercycle size
dc.typeMaster thesis
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.lemacTeoria ergòdica
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37N Applications
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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