On Kuramoto-Sakaguchi-type Fokker-Planck equation with delay

Hirotada Honda; Hirotada Honda

doi:10.3934/nhm.2024001

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 1-23. doi: 10.3934/nhm.2024001

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Research article

On Kuramoto-Sakaguchi-type Fokker-Planck equation with delay

Hirotada Honda ^,

Faculty of Information and Networking for Innovation and Design, Toyo university, Akabanedai 1-7-11, Kita-Ku, Tokyo, Japan

Received: 01 July 2023 Revised: 16 November 2023 Accepted: 30 November 2023 Published: 08 December 2023

Recently, the Kuramoto model with transmission delay has been attracting increasing attention, accompanied by the increase in its practical applications. In this paper, we studied the Kuramoto-Sakaguchi-type Fokker-Planck equation of the above model proposed by Lee et al., in 2009. We proved the global-in-time solvability of the equation under some conditions on the initial data and distribution of delay.
- Kuramoto–Sakaguchi equation,
- synchronization,
- dynamic system,
- Fokker-Planck equation,
- Sobolevel–Slobodetskii space
Citation: Hirotada Honda. On Kuramoto-Sakaguchi-type Fokker-Planck equation with delay[J]. Networks and Heterogeneous Media, 2024, 19(1): 1-23. doi: 10.3934/nhm.2024001

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Abstract

Recently, the Kuramoto model with transmission delay has been attracting increasing attention, accompanied by the increase in its practical applications. In this paper, we studied the Kuramoto-Sakaguchi-type Fokker-Planck equation of the above model proposed by Lee et al., in 2009. We proved the global-in-time solvability of the equation under some conditions on the initial data and distribution of delay.

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