Publication: Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations
dc.contributor.department | N/A | |
dc.contributor.department | Department of Electrical and Electronics Engineering | |
dc.contributor.kuauthor | Şuvak, Önder | |
dc.contributor.kuauthor | Demir, Alper | |
dc.contributor.kuprofile | PhD Student | |
dc.contributor.kuprofile | Faculty Member | |
dc.contributor.other | Department of Electrical and Electronics Engineering | |
dc.contributor.schoolcollegeinstitute | Graduate School of Sciences and Engineering | |
dc.contributor.schoolcollegeinstitute | College of Engineering | |
dc.contributor.yokid | N/A | |
dc.contributor.yokid | 3756 | |
dc.date.accessioned | 2024-11-09T23:34:27Z | |
dc.date.issued | 2010 | |
dc.description.abstract | The 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.indexedby | WoS | |
dc.description.indexedby | Scopus | |
dc.description.issue | 8 | |
dc.description.openaccess | NO | |
dc.description.sponsoredbyTubitakEu | TÜBİTAK | |
dc.description.sponsorship | Turkish Academy of Sciences | |
dc.description.sponsorship | Scientific and Technological Research Council of Turkey (TUBITAK) [104E057] | |
dc.description.sponsorship | 2219 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.volume | 29 | |
dc.identifier.doi | 10.1109/TCAD.2010.2049056 | |
dc.identifier.eissn | 1937-4151 | |
dc.identifier.issn | 0278-0070 | |
dc.identifier.scopus | 2-s2.0-77954872218 | |
dc.identifier.uri | http://dx.doi.org/10.1109/TCAD.2010.2049056 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/12354 | |
dc.identifier.wos | 282543700006 | |
dc.keywords | Isochrons | |
dc.keywords | Oscillators | |
dc.keywords | Phase of an oscillator | |
dc.keywords | Coupled oscillators | |
dc.keywords | Noise | |
dc.keywords | Simulation | |
dc.language | English | |
dc.publisher | IEEE-Inst Electrical Electronics Engineers Inc | |
dc.source | Ieee Transactions on Computer-Aided Design of Integrated Circuits and Systems | |
dc.subject | Computer science | |
dc.subject | Computer architecture | |
dc.subject | Electrical electronics engineering | |
dc.title | Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations | |
dc.type | Journal Article | |
dspace.entity.type | Publication | |
local.contributor.authorid | 0000-0002-0750-8304 | |
local.contributor.authorid | 0000-0002-1927-3960 | |
local.contributor.kuauthor | Şuvak, Önder | |
local.contributor.kuauthor | Demir, Alper | |
relation.isOrgUnitOfPublication | 21598063-a7c5-420d-91ba-0cc9b2db0ea0 | |
relation.isOrgUnitOfPublication.latestForDiscovery | 21598063-a7c5-420d-91ba-0cc9b2db0ea0 |