Phase models and clustering in networks of oscillators with delayed coupling

PHYSICA D-NONLINEAR PHENOMENA

卷:363

Article

Campbell, Sue Ann^1,2  Wang, Zhen¹ 

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Waterloo, Ctr Theoret Neurosci, Waterloo, ON N2L 3G1, Canada

关键词: Time delay;    Neural network;    Oscillators;    Clustering solutions;    Stability;   

DOI  :  10.1016/j.physd.2017.09.004

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free