Open AccessAggregation and disaggregation of active particles on the unit sphere with time-dependent frequencies
Author(s) -
Dohyun Kim,
Jeongho Kim
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021131
Subject(s) - particle dynamics , unit sphere , statistical physics , physics , particle system , dynamics (music) , particle (ecology) , classical mechanics , mathematics , computer science , mathematical analysis , quantum mechanics , molecular dynamics , ecology , acoustics , biology , operating system
We introduce an active swarming model on the sphere which contains additional temporal dynamics for the natural frequency, inspired from the recently introduced modified Kuramoto model, where the natural frequency has its own dynamics. For the attractive interacting particle system, we provide a sufficient framework that leads to the asymptotic aggregation, i.e., all the particles are aggregated to the single point and the natural frequencies also tend to a common value. On the other hand, for the repulsive interacting particle system, we present a sufficient condition for the disaggregation, i.e., the order parameter of the system decays to 0, which implies that the particles are uniformly distributed over the sphere asymptotically. Finally, we also provide several numerical simulation results that support the theoretical results of the paper.