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Frustration tuning and perfect phase synchronization in the Kuramoto-Sakaguchi model

Frustration tuning and perfect phase synchronization in the Kuramoto-Sakaguchi model
Frustration tuning and perfect phase synchronization in the Kuramoto-Sakaguchi model
We present an analysis of conditions under which the dynamics of a frustrated Kuramoto—or Kuramoto-Sakaguchi—model on sparse networks can be tuned to enhance synchronization. Using numerical optimization techniques, linear stability, and dimensional reduction analysis, a simple tuning scheme for setting node-specific frustration parameters as functions of native frequencies and degrees is developed. Finite-size scaling analysis reveals that even partial application of the tuning rule can significantly reduce the critical coupling for the onset of synchronization. In the second part of the paper, a codynamics is proposed, which allows a dynamic tuning of frustration parameters simultaneously with the ordinary Kuramoto dynamics. We find that such codynamics enhance synchronization when operating on slow time scales, and impede synchronization when operating on fast time scales relative to the Kuramoto dynamics.
1539-3755
1-13
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Alexander, Kalloniatis
40e243b7-12b4-4c3b-8f52-98fbc7449840
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Alexander, Kalloniatis
40e243b7-12b4-4c3b-8f52-98fbc7449840

Brede, Markus and Alexander, Kalloniatis (2016) Frustration tuning and perfect phase synchronization in the Kuramoto-Sakaguchi model. Physical Review E, 93 (6), 1-13. (doi:10.1103/PhysRevE.93.062315).

Record type: Article

Abstract

We present an analysis of conditions under which the dynamics of a frustrated Kuramoto—or Kuramoto-Sakaguchi—model on sparse networks can be tuned to enhance synchronization. Using numerical optimization techniques, linear stability, and dimensional reduction analysis, a simple tuning scheme for setting node-specific frustration parameters as functions of native frequencies and degrees is developed. Finite-size scaling analysis reveals that even partial application of the tuning rule can significantly reduce the critical coupling for the onset of synchronization. In the second part of the paper, a codynamics is proposed, which allows a dynamic tuning of frustration parameters simultaneously with the ordinary Kuramoto dynamics. We find that such codynamics enhance synchronization when operating on slow time scales, and impede synchronization when operating on fast time scales relative to the Kuramoto dynamics.

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Accepted/In Press date: 2 June 2016
e-pub ahead of print date: 23 June 2016
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 397481
URI: https://eprints.soton.ac.uk/id/eprint/397481
ISSN: 1539-3755
PURE UUID: 7a11ed29-2224-491e-919a-9ee172310e3e

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Date deposited: 01 Jul 2016 13:42
Last modified: 09 Jan 2018 18:01

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Contributors

Author: Markus Brede
Author: Kalloniatis Alexander

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