SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2103-2134, January 2020.
In this paper, we study an agent-based interacting particle system with attractive and singular repulsive forces. We prove the collision avoidance between particles from different groups due to repulsive forces. Moreover, we provide a sufficient condition for the emergence of asymptotic consensus in the same group and separation for different groups. We consider the one-dimensional and multidimensional cases separately since they exhibit different dynamics. Numerical simulations are performed to support our theoretical results.

中文翻译：

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具有吸引力和奇异排斥力的基于主体的模型中共识和分离的出现

SIAM应用动力系统杂志，第19卷，第3期，第2103-2134页，2020
年1月。在本文中，我们研究了具有吸引力和奇异排斥力的基于主体的相互作用粒子系统。我们证明了排斥力导致不同组的粒子之间避免碰撞。此外，我们为同一组中渐近共识的出现和不同组之间的分离提供了充分的条件。由于它们表现出不同的动态性，因此我们分别考虑一维和多维情况。进行数值模拟以支持我们的理论结果。