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Controlling and enhancing synchronisation through adaptive phase lags

Controlling and enhancing synchronisation through adaptive phase lags
Controlling and enhancing synchronisation through adaptive phase lags
We compare two methods for controlling synchronisation in the Kuramoto model on an undirected network. The first is by driving selected oscillators at a desired frequency by coupling to an external driver, and the second is by including adaptive lags -- or dynamical frustrations -- within the Kuramoto interactions, with the lags evolving according to a dynamics as a function of the reference frequency with an associated time-constant. Performing numerical simulations with random regular graphs, we find that above a certain connectivity driving via adaptive lags allows for stronger alignment to the external frequency at lower value of the time-constant compared to the corresponding coupling strength for the externally driven model. Numerical results are backed up by equilibrium analysis based on a fixed point ansatz for frequency synchronised clusters where we solve the spectrum of the associated Jacobian matrix. We find that at low connectivity the external driving mechanism is successful down to lower densities of controlled oscillators where the adaptive lag approach is Lyapunov unstable at all densities. As connectivity increases, however, the adaptive lag mechanism shows stability over similar ranges of density to the external driving and proves superior in terms of tighter splays of oscillators. In particular, the threshold for instability for the adaptive lag model shows robustness against variations in the associated time constant down to lower densities of controlled oscillators. A simple intuitive model emerges based on the interaction between splayed clusters close to a critical point.
1539-3755
Kalloniatis, Alexander
8ee212af-cddd-4752-ab7b-f21165c3aaf8
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Kalloniatis, Alexander
8ee212af-cddd-4752-ab7b-f21165c3aaf8
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7

Kalloniatis, Alexander and Brede, Markus (2019) Controlling and enhancing synchronisation through adaptive phase lags. Physical Review E, 99, [032303]. (doi:10.1103/PhysRevE.99.032303).

Record type: Article

Abstract

We compare two methods for controlling synchronisation in the Kuramoto model on an undirected network. The first is by driving selected oscillators at a desired frequency by coupling to an external driver, and the second is by including adaptive lags -- or dynamical frustrations -- within the Kuramoto interactions, with the lags evolving according to a dynamics as a function of the reference frequency with an associated time-constant. Performing numerical simulations with random regular graphs, we find that above a certain connectivity driving via adaptive lags allows for stronger alignment to the external frequency at lower value of the time-constant compared to the corresponding coupling strength for the externally driven model. Numerical results are backed up by equilibrium analysis based on a fixed point ansatz for frequency synchronised clusters where we solve the spectrum of the associated Jacobian matrix. We find that at low connectivity the external driving mechanism is successful down to lower densities of controlled oscillators where the adaptive lag approach is Lyapunov unstable at all densities. As connectivity increases, however, the adaptive lag mechanism shows stability over similar ranges of density to the external driving and proves superior in terms of tighter splays of oscillators. In particular, the threshold for instability for the adaptive lag model shows robustness against variations in the associated time constant down to lower densities of controlled oscillators. A simple intuitive model emerges based on the interaction between splayed clusters close to a critical point.

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Kalloniatis-Brede-2017-adaptivelags-PRE-v2 - Accepted Manuscript
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Accepted/In Press date: 1 March 2019
Published date: 7 March 2019
Additional Information: in press

Identifiers

Local EPrints ID: 429036
URI: http://eprints.soton.ac.uk/id/eprint/429036
ISSN: 1539-3755
PURE UUID: bc8a15c5-d7fe-41d3-9c79-faf1aee451a6

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Date deposited: 19 Mar 2019 17:30
Last modified: 06 Oct 2020 20:03

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Author: Alexander Kalloniatis
Author: Markus Brede

University divisions

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