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dc.contributor.authorPérez Cervera, Alberto
dc.contributor.authorMartínez-Seara Alonso, M. Teresa
dc.contributor.authorHuguet Casades, Gemma
dc.contributor.otherUniversitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationPerez, A.; Martinez-Seara, T.; Huguet, G. A geometric approach to phase response curves and its numerical computation through the parameterization method. "Journal of nonlinear science", 1 Gener 2019, vol. 29, p. 2877-2910.
dc.descriptionThe final publication is available at
dc.description.abstractThe phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new approach to PRCs based on the parameterization method. The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. We demonstrate the relationship between the internal dynamics of this invariant curve and the PRC, which yields a method to numerically compute the PRCs. Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. The invariant curve and its dynamics will be computed by means of the parameterization method consisting of solving an invariance equation. We show that the method to compute the PRC can be extended beyond the breakdown of the curve by means of introducing a modified invariance equation. The method also computes the amplitude response functions (ARCs) which provide information on the displacement away from the oscillator due to the effects of the perturbation. Finally, we apply the method to several classical models in neuroscience to illustrate how the results herein extend the framework of computation and interpretation of the PRC and ARC for perturbations of large amplitude and not necessarily pulsatile.
dc.format.extent34 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherPhase Response Curves
dc.subject.otherPhase equation
dc.subject.otherParameterization method
dc.titleA geometric approach to phase response curves and its numerical computation through the parameterization method
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorPerez, A.; Martinez-Seara, Tere; Huguet, G.
local.citation.publicationNameJournal of nonlinear science

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