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dc.contributor.authorBonet Revés, Carles
dc.contributor.authorJeffrey, Mike R.
dc.contributor.authorMartín de la Torre, Pablo
dc.contributor.authorOlm Miras, Josep Maria
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2021-09-17T07:48:13Z
dc.date.available2023-11-01T01:32:27Z
dc.date.issued2021-11-01
dc.identifier.citationBonet, C. [et al.]. Ageing of an oscillator due to frequency switching. "Communications in nonlinear science and numerical simulation", 1 Novembre 2021, vol. 102, p. 105950:1-105950:26.
dc.identifier.issn1007-5704
dc.identifier.urihttp://hdl.handle.net/2117/351568
dc.description.abstractIf an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs either: (i) between two driving forces which have different frequencies, or (ii) as a single forcing whose frequency switches between two values. The difference is subtle, but its effect on the long term behaviour is severe, and occurs because the expressions of (i) and (ii) are linear and nonlinear, respectively, in terms of a discontinuous quantity (e.g. a sign or Heaviside step function) that represents the switch between frequencies. In scenario (i) the oscillator can be described as a Filippov system, and we will show it has a stable periodic orbit. In scenario (ii) the oscillator exhibits hidden dynamics, which lies outside the theory of Filippov’s systems, and causes the system to be increasingly (as time passes) dominated by sliding along the frequency-switching threshold, and in particular if periodic orbits do exist, they too exhibit sliding. We show that the behaviour persists, at least asymptotically, if the systems are regularized (i.e. if the switch is modelled in the manner of (i) or (ii) but with a smooth rather than discontinuous transition).
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDynamics
dc.subject.lcshMathematical analysis
dc.subject.lcshDifferential equations
dc.subject.lcshNumerical analysis
dc.subject.otherNonsmooth
dc.subject.otherFilippov
dc.subject.otherHidden dynamics
dc.subject.otherPiecewise
dc.subject.otherAgeing
dc.subject.otherSwitching
dc.subject.otherMixed-mode
dc.titleAgeing of an oscillator due to frequency switching
dc.typeArticle
dc.subject.lemacDinàmica
dc.subject.lemacAnàlisi matemàtica
dc.subject.lemacEquacions diferencials
dc.subject.lemacAnàlisi numèrica
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.contributor.groupUniversitat Politècnica de Catalunya. ACES - Control Avançat de Sistemes d'Energia
dc.identifier.doi10.1016/j.cnsns.2021.105950
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S1007570421002628
dc.rights.accessOpen Access
local.identifier.drac32027211
dc.description.versionPostprint (author's final draft)
local.citation.authorBonet, C.; Jeffrey, M.; Martin, P.; Olm, Josep M.
local.citation.publicationNameCommunications in nonlinear science and numerical simulation
local.citation.volume102
local.citation.startingPage105950:1
local.citation.endingPage105950:26


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