Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256297 | Physica D: Nonlinear Phenomena | 2018 | 12 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sue Ann Campbell, Zhen Wang,