A Phase Model with Large Time Delayed Coupling

Simple item page
dc.contributor.authorAl-Darabsah, Islam
dc.contributor.authorCampbell, Sue Ann
dc.date.accessioned2022-04-22T20:33:35Z
dc.date.available2022-04-22T20:33:35Z
dc.date.issued2020-10
dc.description.abstractWe consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has an explicit delay and phase shift in the argument of the phases and connection function, respectively. Using the phase model, we prove that for any type of oscillators and any coupling, the in-phase and anti-phase phase-locked solutions always exist and give conditions for their stability. We show that for small delay these solutions are unique, but with large enough delay multiple solutions of each type with different frequencies may occur. We give conditions for the existence and stability of other types of phase-locked solutions. We discuss the various bifurcations that can occur in the phase model as the time delay is varied. The results of the phase model analysis are applied to Morris–Lecar oscillators with diffusive coupling and compared with numerical studies of the full system of delay differential equations. We also consider the case of small time delay and compare the results with the existing ones in the literature.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canadaen
dc.identifier.urihttps://doi.org/10.48550/arXiv.1910.03435
dc.identifier.urihttp://hdl.handle.net/10012/18166
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofseriesPhysica. D;
dc.subjectcoupled oscillatorsen
dc.subjectlarge time delayen
dc.subjectsynchronizationen
dc.subjectphase-lockingen
dc.titleA Phase Model with Large Time Delayed Couplingen
dc.typeArticleen
dcterms.bibliographicCitationAl-Darabsah, I., & Campbell, S. A. (2020). A Phase Model with Large Time Delayed Coupling. Physica D: Nonlinear Phenomena, 411, 132559. https://doi.org/10.1016/j.physd.2020.132559en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Applied Mathematicsen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
A Phase Model with Large Time Delayed Coupling.pdf
Size:
5.55 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
4.47 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Waterloo Research
Applied Mathematics