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

TL;DR

This paper demonstrates the emergence of a periodically rotating one-point cluster in a thermomechanical Cucker-Smale ensemble confined in a harmonic potential, combining analytical energy estimates with numerical simulations.

Contribution

It introduces the novel phenomenon of periodic rotation in TCS ensembles within harmonic potentials, which was not observed in previous models without external forces.

Findings

Emergence of a rotating one-point cluster in TCS model

Analytical and numerical results agree on cluster behavior

Periodic rotation depends on system parameters

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.