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Comment on “Low-dimensional behavior of generalized Kuramoto model” by S. Ameli and K. A. Samani

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Abstract

In the paper Ameli and Samani (Nonlinear Dyn https://doi.org/10.1007/s11071-022-07703-0, 2022), the authors formulate low-dimensional evolutions of the macroscopic order parameters in the generalized Kuramoto model, in which the quenched disorder of the heterogeneous natural frequencies and coupling strength are correlated via a weighted absolute value function. The authors state that the collective dynamics, as well as the global bifurcation of various attractors, can be delineated in the framework of the low-dimensional manifold. We argue that such low-dimensional descriptions for the frequency-weighted coupling are not correct in general. This contradiction is explained from several aspects, including the Ott-Antonsen reduction and the forward (backward) critical points corresponding to the onset (vanishing) of synchrony. Remarkably, we uncover that the singularity of the frequency-weighted coupling forbids the analytical continuation, but can vastly simplify the coherent behaviors of the system. Importantly, we justify that our analysis can be extended to a wide class of systems involving the frequency-weighted coupling scheme.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11905068) and the Scientific Research Funds of Huaqiao University (Grant No. ZQN-810).

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  1. Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Can Xu

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  1. Can Xu
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Correspondence to Can Xu.

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Xu, C. Comment on “Low-dimensional behavior of generalized Kuramoto model” by S. Ameli and K. A. Samani. Nonlinear Dyn 111, 6915–6920 (2023). https://doi.org/10.1007/s11071-022-08124-9

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