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

Abstract

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.

Keywords:

• Cucker-Smale model
• collision-avoidance
• flocking
• inter-particle force

2020 Mathematics Subject Classifications:

• 93A15
• 93C10
• 76N10

Acknowledgments

The authors would like to thank two anonymous referees for their valuable comments and suggestions on this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11671011].