Traveling Waves in the McKean-Vlasov Equation under Sakaguchi-Kuramoto Interaction with Phase Frustration
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917419172233216 |
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| author | Vukadinovic, Jesenko |
| author_facet | Vukadinovic, Jesenko |
| contents | We study the McKean-Vlasov equation for weakly coupled oscillators subject to the Sakaguchi-Kuramoto interaction. While the Kuramoto interaction provides a good approximation for small, densely connected networks, time delays in larger networks lead to symmetry-breaking phase offsets (frustrations). The Sakaguchi-Kuramoto interaction is the simplest such generalization, featuring a single frustration parameter. We establish the existence of a continuous global phase transition from incoherence to coherence, in the form of a propagating asymmetrically extended von Mises probability distribution function (AvMPDF). The corresponding traveling wave equation reduces to a system of two equations in two unknowns: the order parameter for the AvMPDF and the wave speed. The analysis relies on an appropriate asymmetrical extension of the modified Bessel function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_18059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Traveling Waves in the McKean-Vlasov Equation under Sakaguchi-Kuramoto Interaction with Phase Frustration Vukadinovic, Jesenko Analysis of PDEs Dynamical Systems We study the McKean-Vlasov equation for weakly coupled oscillators subject to the Sakaguchi-Kuramoto interaction. While the Kuramoto interaction provides a good approximation for small, densely connected networks, time delays in larger networks lead to symmetry-breaking phase offsets (frustrations). The Sakaguchi-Kuramoto interaction is the simplest such generalization, featuring a single frustration parameter. We establish the existence of a continuous global phase transition from incoherence to coherence, in the form of a propagating asymmetrically extended von Mises probability distribution function (AvMPDF). The corresponding traveling wave equation reduces to a system of two equations in two unknowns: the order parameter for the AvMPDF and the wave speed. The analysis relies on an appropriate asymmetrical extension of the modified Bessel function. |
| title | Traveling Waves in the McKean-Vlasov Equation under Sakaguchi-Kuramoto Interaction with Phase Frustration |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2510.18059 |