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Controlling synchronisation through adaptive phase lags

Markus Brede, Alexander Kalloniatis
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 linking to an external driver, and the second is by including adaptive lags within the
Kuramoto interactions, where the lags evolve according to a dynamics involving the reference frequency.
Performing numerical simulations, we find that driving via adaptive lags allows for stronger alignment to the external driver at lower cost. Numerical results are backed up by equilibrium analysis based on a fixed point ansatz assuming frequency synchronised clusters and solving the spectrum of the associated
Jacobian. A simple intuitive model emerges based on the interaction between splayed clusters close to a critical point.
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