Collision-avoidance, aggregation and velocity-matching in a Cucker-Smale-type model

By introducing an attractive-repulsive force in Cucker-Smale model, the dynamic behaviour of multi-agent system is studied. The Cucker-Smale-type model considered in this paper has three properties: collision-avoidance, aggregation and velocity-matching, which are significant rules in dynamic behaviour of multi-agent systems. Results of collision-avoidance, flocking and swarming are given respectively. Different from previous work, the Cucker-Smale-type model shows unconditional and conditional swarming respectively when weight function f = (r- d(0))(-theta) of the attractive-repulsive force satisfies 0 is an element of [1, 3] and 0 > 3. Moreover, for the case f = r(-theta),theta >= 2, results of collision-avoidance tell us that there exists a positive lower bound of relative distance, which improve previous work of collision-avoidance. (C) 2021 Elsevier Ltd. All rights reserved.