Document Type
Article
Department
Mathematics
Publication Date
6-2016
Abstract
We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.
Publication Title
Physica D
Volume
323-324
First Page
40
Last Page
48
DOI
10.1016/j.physd.2015.10.015
Comments
Published as:
Per Skardal. “Erosion of Synchronization: Coupling Heterogeneity and Network Structure.” Physica D 323-324 (2016): 40.
Author's accepted manuscript provided by the Trinity College Digital Repository in accordance with the publisher's distribution policies.