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dc.contributor.authorDankowicz, H
dc.contributor.authorSieber, J
dc.date.accessioned2022-03-09T08:57:17Z
dc.date.issued2022-04-22
dc.date.updated2022-03-08T15:13:17Z
dc.description.abstractThis paper presents a rigorous framework for the continuation of solutions to nonlinear constraints and the simultaneous analysis of the sensitivities of test functions to constraint violations at each solution point using an adjoint-based approach. By the linearity of a problem Lagrangian in the associated Lagrange multipliers, the formalism is shown to be directly amenable to analysis using the COCO software package, specifically its paradigm for staged problem construction. The general theory is illustrated in the context of algebraic equations and boundary-value problems, with emphasis on periodic orbits in smooth and hybrid dynamical systems, and quasiperiodic invariant tori of flows. In the latter case, normal hyperbolicity is used to prove the existence of continuous solutions to the adjoint conditions associated with the sensitivities of the orbital periods to parameter perturbations and constraint violations, even though the linearization of the governing boundary-value problem lacks a bounded inverse, as required by the general theory. An assumption of transversal stability then implies that these solutions predict the asymptotic phases of trajectories based at initial conditions perturbed away from the torus. Example COCO code is used to illustrate the minimal additional investment in setup costs required to append sensitivity analysis to regular parameter continuation.en_GB
dc.description.sponsorshipEngineering and Physical Sciences Research Council (EPSRC)en_GB
dc.identifier.citationPublished online 22 April 2022en_GB
dc.identifier.doi10.3934/jcd.2022006
dc.identifier.grantnumberEP/N023544/1en_GB
dc.identifier.grantnumberEP/V04687X/1en_GB
dc.identifier.urihttp://hdl.handle.net/10871/128975
dc.identifierORCID: 0000-0002-9558-1324 (Sieber, Jan)
dc.language.isoenen_GB
dc.publisherAmerican Institute of Mathematical Sciencesen_GB
dc.relation.urlhttps://github.com/jansieber/adjoint-sensitivity2022-suppen_GB
dc.rights© 2022 American Institute of Mathematical Sciences
dc.subjecthybrid systemsen_GB
dc.subjectnumerical continuationen_GB
dc.subjectconstraint Lagrangianen_GB
dc.subjectpersistenceen_GB
dc.subjectsoftware implementationen_GB
dc.titleSensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint methoden_GB
dc.typeArticleen_GB
dc.date.available2022-03-09T08:57:17Z
dc.identifier.issn2158-2491
dc.descriptionThis is the author accepted manuscript. The final version is available from the American Institute of Mathematical Sciences via the DOI in this recorden_GB
dc.descriptionCode availability: The code included in this paper constitutes fully executable scripts. Complete code, including that used to generate the results in Fig. 1, is available at https://github.com/jansieber/adjoint-sensitivity2022-supp.en_GB
dc.identifier.journalJournal of Computational Dynamicsen_GB
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserveden_GB
dcterms.dateAccepted2022-03-03
rioxxterms.versionAMen_GB
rioxxterms.licenseref.startdate2022-03-03
rioxxterms.typeJournal Article/Reviewen_GB
refterms.dateFCD2022-03-08T15:13:21Z
refterms.versionFCDAM
refterms.dateFOA2022-05-04T15:08:42Z
refterms.panelBen_GB


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