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dc.contributorGuillamon Grabolosa, Antoni
dc.contributor.authorMartínez Añón, Kevin
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2020-10-22T12:53:21Z
dc.date.available2020-10-22T12:53:21Z
dc.date.issued2020-10
dc.identifier.urihttp://hdl.handle.net/2117/330639
dc.description.abstractA vast literature has been devoted throughout the years to the construction of both a phase and an amplitude response function that help us study the effects of external stimuli on the dynamics of oscillatory systems. Results trying to reproduce these techniques in the case of damped oscillations have come up recently. Thus, adhering to this recent trend, in this Master's Thesis we complete the study on damped oscillations initiated last year by my colleague Román Moreno in his own Master's Thesis and, based on it, we present a novel optimal control algorithm for the induction of sustained periodic oscillations out of a damped oscillation using a minimum-energy input. The positive results obtained can be seen, from a theoretical point of view, as a deterministic method for the generation of stable structures in systems where they were initially not present; and, from a more practical perspective, they may open the door for therapeutic studies of some neuropathologies when applied to some neuron models in neuroscience.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherDamped oscillations
dc.subject.otherStrong focus
dc.subject.otherIsochronicity
dc.subject.otherIsochrons
dc.subject.otherIsostables
dc.subject.otherAugmented phase reduction
dc.subject.otherPhase response function
dc.subject.otherAmplitude response function
dc.subject.otherOptimal control
dc.subject.otherEuler-Lagrange equations
dc.subject.otherNeuron models
dc.subject.otherFitzhugh-Nagumo model.
dc.titleOptimal control over damped oscillations via response curves
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.identifier.slugFME-1990
dc.rights.accessOpen Access
dc.date.updated2020-10-21T05:27:45Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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