Cucker–Smale flocking with randomly failed interactions

We consider the Cucker–Smale model consisting of interacted particles involving random failure. More precisely, each pair of neighboring agents can fail to interact with a certain probability. Two cases are considered: undirected connected interactions and directed rooted interactions. Our results show that the unconditional flocking for long-range communication rate is still true independently of the failure rate probability. For short-range communication rate, conditional flocking can be established. These results, together with the previous study of Dalmao and Mordecki (2012) [8] , suggest that the C–S flocking system under various interaction topologies can endure random failure in interactions.