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The communication topology among the agents is switching and agents receive information within a critical bounded distance. As new observations, we show that the desired protocol system undergoes consensus and swarming behaviours when 1 is a simple eigenvalue of the adjacency matrix. In this case, both final velocity and final relative position are formulated. Simulation results show the effectiveness of the proposed protocol.<\/jats:p>","DOI":"10.1515\/auto-2020-0068","type":"journal-article","created":{"date-parts":[[2021,5,27]],"date-time":"2021-05-27T15:43:46Z","timestamp":1622130226000},"page":"472-484","source":"Crossref","is-referenced-by-count":3,"title":["Consensus and swarming behaviors for a proportional-derivative system with a cut-off interaction"],"prefix":"10.1515","volume":"69","author":[{"given":"Jun","family":"Wu","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics , Changsha University of Science Technology , Changsha , , P.R. 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