Emergent Behaviors of Thermodynamic Cucker--Smale Particles
Seung‐Yeal Ha, Jeongho Kim, Tommaso Ruggeri · SIAM Journal on Mathematical Analysis · 2018
We study the flocking dynamics of a generalized Cucker--Smale (C-S) model for thermodynamic particles. The original C-S model deals with flocking dynamics of mechanical particles, in which the position and momentum are only kinematic observables. Thus, the C-S model cannot describe a phenomenon caused by different “internal energy (temperatures)” between particles. Recently, a new particle model for flocking was proposed to model a flocking dynamics in an ensemble of thermodynamic particles on time-independent communication networks, where spatial dependence in the communication was neglected. In this paper, we extend a thermodynamically consistent particle to incorporate communications depending on the positions of the particle and study its asymptotic dynamics, such as formation and nonexistence of mono-cluster flockings in terms of an initial configuration, coupling strength, and ansatz of the communication weights.