Flocking Behaviors under Hierarchical Leadership of Thermodynamic Cucker–Smale Particles with Multiplicative White Noise and Perturbation

The thermodynamic Cucker–Smale model (TCS model) describes dynamic consistency caused by different temperatures between multi-agent particles. This paper studies the flocking behaviors of the TCS model with multiplicative white noise under hierarchical leadership. First, we introduce the corresponding model of two particles. Then, by using mathematical induction and considering the properties of differential functions, it is proved that, under certain conditions, the group can achieve flocking. Finally, we verify the conclusion through numerical simulation results. Similarly, this paper studies the above model with perturbation functions.