Publication:
Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations

dc.contributor.departmentN/A
dc.contributor.departmentDepartment of Electrical and Electronics Engineering
dc.contributor.kuauthorŞuvak, Önder
dc.contributor.kuauthorDemir, Alper
dc.contributor.kuprofilePhD Student
dc.contributor.kuprofileFaculty Member
dc.contributor.otherDepartment of Electrical and Electronics Engineering
dc.contributor.schoolcollegeinstituteGraduate School of Sciences and Engineering
dc.contributor.schoolcollegeinstituteCollege of Engineering
dc.contributor.yokidN/A
dc.contributor.yokid3756
dc.date.accessioned2024-11-09T23:34:27Z
dc.date.issued2010
dc.description.abstractThe notion of isochrons for oscillators, introduced by Winfree and thereon heavily utilized in mathematical biology, were instrumental in introducing a notion of generalized phase and form the basis for oscillator perturbation analyses. Computing isochrons is a hard problem, existing brute-force methods incurring exponential complexity. In this paper, we present a precise and carefully developed theory and numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the techniques needed for computing only local linear approximations. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple analytically calculable case, test our methods on complex oscillators, and show how quadratic approximations of isochrons can be used in formulating accurate, novel phase computation schemes and finally allude to second-order accurate compact phase macromodels. Oscillator studies seem to have progressed independently in electronics and biology. Even though analyses in electronics did not make use of the notion of isochrons, similar models and methods, expressed in totally different terminologies, have been developed in both disciplines. In this paper, we also reveal the connection between oscillator analysis work in these two seemingly disparate disciplines.
dc.description.indexedbyWoS
dc.description.indexedbyScopus
dc.description.issue8
dc.description.openaccessNO
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipTurkish Academy of Sciences
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK) [104E057]
dc.description.sponsorship2219 Research Fellowship Program This work was supported by the Turkish Academy of Sciences GEBIP Program, by the Scientific and Technological Research Council of Turkey (TUBITAK), under Project 104E057, and by the 2219 Research Fellowship Program. This paper was recommended by Associate Editor H. E. Graeb.
dc.description.volume29
dc.identifier.doi10.1109/TCAD.2010.2049056
dc.identifier.eissn1937-4151
dc.identifier.issn0278-0070
dc.identifier.scopus2-s2.0-77954872218
dc.identifier.urihttp://dx.doi.org/10.1109/TCAD.2010.2049056
dc.identifier.urihttps://hdl.handle.net/20.500.14288/12354
dc.identifier.wos282543700006
dc.keywordsIsochrons
dc.keywordsOscillators
dc.keywordsPhase of an oscillator
dc.keywordsCoupled oscillators
dc.keywordsNoise
dc.keywordsSimulation
dc.languageEnglish
dc.publisherIEEE-Inst Electrical Electronics Engineers Inc
dc.sourceIeee Transactions on Computer-Aided Design of Integrated Circuits and Systems
dc.subjectComputer science
dc.subjectComputer architecture
dc.subjectElectrical electronics engineering
dc.titleQuadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.authorid0000-0002-0750-8304
local.contributor.authorid0000-0002-1927-3960
local.contributor.kuauthorŞuvak, Önder
local.contributor.kuauthorDemir, Alper
relation.isOrgUnitOfPublication21598063-a7c5-420d-91ba-0cc9b2db0ea0
relation.isOrgUnitOfPublication.latestForDiscovery21598063-a7c5-420d-91ba-0cc9b2db0ea0

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