In this paper, we derive a kinetic description of swarming particle dynamics in an interacting multi-agent system featuring emerging leaders and followers. Agents are classically characterized by their position and velocity plus a continuous parameter quantifying their degree of leadership. The microscopic processes ruling the change of velocity and degree of leadership are independent, non-conservative and non-local in the physical space, so as to account for long-range interactions. Out of the kinetic description, we obtain then a macroscopic model under a hydrodynamic limit reminiscent of that used to tackle the hydrodynamics of weakly dissipative granular gases, thus relying in particular on a regime of small non-conservative and short-range interactions. Numerical simulations in one- and two-dimensional domains show that the limiting macroscopic model is consistent with the original particle dynamics and furthermore can reproduce classical emerging patterns typically observed in swarms.

翻译：本文推导了具有涌现领导者和追随者的交互多智能体系统中群体粒子动力学的动力学描述。智能体经典地由其位置和速度以及一个连续参数（量化其领导程度）来表征。控制速度和领导程度变化的微观过程是独立的、非保守的且物理空间非局部的，以考虑长程相互作用。基于动力学描述，我们在流体动力学极限下获得了宏观模型，该极限让人联想到用于处理弱耗散颗粒气体流体动力学的模型，特别是依赖于小非保守和短程相互作用的状态。一维和二维域中的数值模拟表明，该极限宏观模型与原始粒子动力学一致，并且能够重现群体中典型观察到的经典涌现模式。