Emergence of the consensus and separation in an agent-based model with attractive and singular repulsive forces. (English) Zbl 1475.93102
Summary: 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.
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