Emergence of a periodically rotating one-point cluster in a thermodynamic Cucker-Smale ensemble

Cho, Hangjun; Du, Linglong; Ha, Seung-Yeal

doi:10.1090/qam/1602

Authors: Hangjun Cho, Linglong Du and Seung-Yeal Ha
Journal: Quart. Appl. Math. 80 (2022), 1-22
MSC (2020): Primary 34D05, 70F99, 74A15
DOI: https://doi.org/10.1090/qam/1602
Published electronically: November 16, 2021
MathSciNet review: 4360547
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Abstract: We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under various frameworks formulated in terms of initial configuration, system parameters and network topologies. Moreover, the TCS model does not exhibit rotating motions in the absence of an external force field. In this paper, we show the emergence of periodically rotating one-point cluster for the TCS model in a harmonic potential field using elementary energy estimates and continuity argument. We also provide several numerical simulations and compare them with analytical results.

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