Phase models and clustering in networks of oscillators with delayed coupling
MetadataShow full item record
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.
Cite this version of the work
Sue Ann Campbell, Zhen Wang (2017). Phase models and clustering in networks of oscillators with delayed coupling. UWSpace. http://hdl.handle.net/10012/12630
The following license files are associated with this item: