An Extended Kuramoto Model for Frequency and Phase Synchronization in Delay-Free Networks with Finite Number of Agents
<|reference_start|>An Extended Kuramoto Model for Frequency and Phase Synchronization in Delay-Free Networks with Finite Number of Agents: Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase synchronization - something the standard Kuramoto model can not provide for a finite number of agents. In this case, a remaining phase difference is necessary to offset differences of the natural frequencies. Setting the Kuramoto model into the context of dynamic consensus and making use of the $n$th order discrete average consensus algorithm, this paper extends the standard Kuramoto model in such a way that frequency and phase synchronization are separated. This in turn leads to an algorithm achieve the required frequency and phase synchronization also for a finite number of agents. Simulations show the viability of this extended Kuramoto model.<|reference_end|>
@article{bathelt2024an,
    title={An Extended Kuramoto Model for Frequency and Phase Synchronization in
  Delay-Free Networks with Finite Number of Agents},
    author={Andreas Bathelt, Vimukthi Herath and Thomas Dallmann},
    journal={arXiv preprint arXiv:2403.13440},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.13440},
    primaryClass={eess.SY cs.SY eess.SP}
}