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Adaptive lags offer superior synchronization control in Kuramoto models at higher network connectivity compared to external driving. This method achieves stronger alignment with less time constant tuning, outperforming traditional methods.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • The Kuramoto model is a fundamental tool for studying synchronization phenomena in coupled oscillator systems.
  • Controlling synchronization is crucial in various fields, including neuroscience, power grids, and social dynamics.
  • Existing control methods often rely on external forcing or modifications to oscillator interactions.

Purpose of the Study:

  • To compare the efficacy of two distinct control strategies for achieving frequency synchronization in the Kuramoto model.
  • To investigate the influence of network connectivity and control parameters on synchronization performance.
  • To analyze the stability and robustness of each control method under varying conditions.

Main Methods:

  • Numerical simulations were conducted on random regular graphs representing undirected networks.
  • Two control methods were implemented: external driving of selected oscillators and adaptive lags (dynamical frustrations) within interactions.
  • Equilibrium analysis using a fixed-point ansatz and Jacobian matrix spectrum was employed to support simulation results.

Main Results:

  • Above a critical network connectivity, adaptive lags achieve stronger alignment to an external frequency with lower time constant requirements than external driving.
  • At low connectivity, external driving is effective at lower densities of controlled oscillators, while adaptive lags show instability.
  • As connectivity increases, adaptive lags demonstrate comparable stability to external driving but yield tighter oscillator splay and robustness against parameter variations.

Conclusions:

  • Adaptive lags represent a powerful and robust method for controlling synchronization in the Kuramoto model, particularly in highly connected networks.
  • The study reveals a trade-off between control methods based on network connectivity and desired synchronization precision.
  • A simplified model elucidates the interaction dynamics of synchronized clusters near critical points.