- Title
- Synchronization properties of trees in the kuramoto model
- Creator
- Dekker, Anthony; Taylor, Richard
- Date
- 2013
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/54306
- Identifier
- vital:5152
- Identifier
-
https://doi.org/10.1137/120899728
- Identifier
- ISSN:1536-0040
- Abstract
- We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For several classes of tree, and for both uniform and Gaussian vertex frequency distributions, we provide tight closed-form bounds and empirical expressions for the expected value of the critical coupling. We also provide several bounds on the expected value of the critical coupling for all trees. Finally, we show that for a given set of vertex frequencies, there is a rearrangement of oscillator frequencies for which the critical coupling is bounded by the spread of frequencies. © 2013 Society for Industrial and Applied Mathematics.; C1
- Relation
- SIAM Journal on Applied Dynamical Systems Vol. 12, no. 2 (2013), p. 596-617
- Rights
- Copyright Society for Industrial and Applied Mathematics.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; Kuramoto model; Synchronization; Tree
- Full Text
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