dc.contributor.author | Campbell, Sue Ann | |
dc.contributor.author | Wang, Zhen | |
dc.date.accessioned | 2017-11-16 17:24:51 (GMT) | |
dc.date.available | 2017-11-16 17:24:51 (GMT) | |
dc.date.issued | 2017-09-19 | |
dc.identifier.uri | http://dx.doi.org/10.1016/j.physd.2017.09.004 | |
dc.identifier.uri | http://hdl.handle.net/10012/12630 | |
dc.description | The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.physd.2017.09.004 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | en |
dc.description.abstract | We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies. | en |
dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada [171089-2012] | en |
dc.language.iso | en | en |
dc.publisher | Elsevier | en |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Clustering Solutions | en |
dc.subject | Neural Network | en |
dc.subject | Oscillators | en |
dc.subject | Stability | en |
dc.subject | Time Delay | en |
dc.title | Phase models and clustering in networks of oscillators with delayed coupling | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Campbell, S. A., & Wang, Z. (2017). Phase models and clustering in networks of oscillators with delayed coupling. Physica D: Nonlinear Phenomena. https://doi.org/10.1016/j.physd.2017.09.004 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Applied Mathematics | en |
uws.typeOfResource | Text | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |