2019/09/08 by Xiongtao Zhang, Tingting Zhu, Zhang, Xiongtao +1
Computer Science · Engineering · Environmental Science · #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.1909.03358
openalex publication_date 2019/09/08 · openalex created_date 2019/09/12 · openalex updated_date 2026/07/28
In this paper, we will study the emergent dynamics of the discrete Kuramoto model for generic initial data. This is an extension of the previous work S.-Y. Ha et al. (2019), in which the initial configurations are supposed to be within a half circle. More precisely, we will provide the theory of discrete gradient flow which can be applied to general Euler iteration scheme. Therefore, as a direct application, we conclude the emergence of synchronization of discrete Kuramoto model. Moreover, we obtain for small mesh size that, the synchronization will occur exponentially fast for initial data in A1 (see definition in (4.1)).