Phase models and clustering in networks of oscillators with delayed coupling
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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.
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Sue Ann Campbell, Zhen Wang (2017). Phase models and clustering in networks of oscillators with delayed coupling. UWSpace. http://hdl.handle.net/10012/12630
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