Phase models and clustering in networks of oscillators with delayed coupling
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Date
2017-09-19
Authors
Campbell, Sue Ann
Wang, Zhen
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
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.
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/
Keywords
Clustering Solutions, Neural Network, Oscillators, Stability, Time Delay