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In this paper, by introducing a singular inter-particle force into Cucker-Smale model, the result of collision-avoidance is obtained. The inter-particle force can switch between attractive and repelling with the change of the inner product of relative velocities and positions, which is different from the force repelling only and more in line with the internal binding force of multi-agent systems. Through the establishing of Lyapunov functions, we show that the system can avoid collisions when initial positions are non-collisional. Moreover, for Cucker-Smale model with the singular inter-particle force, results about flocking behaviour are presented.

A singular inter-particle force in Cucker-Smale model to avoid collisions