Journal of Statistical Physics

, Volume 171, Issue 2, pp 345–360 | Cite as

Flocking of the Motsch–Tadmor Model with a Cut-Off Interaction Function

  • Chunyin Jin


In this paper, we study the flocking behavior of the Motsch–Tadmor model with a cut-off interaction function. Our analysis shows that connectedness is important for flocking of this kind of model. Fortunately, we get a sufficient condition imposed only on the model parameters and initial data to guarantee the connectedness of the neighbor graph associated with the system. Then we present a theoretical analysis for flocking, and show that the system achieves consensus at an exponential rate.


Motsch–Tadmor model Cucker–Smale model Flocking Stochastic matrix Neighbor graph 

Mathematics Subject Classification

34A36 34D06 34F15 34K25 70E55 



The author would like to thank the referee for detailed comments, which benefit him a lot and improve the presentation of this paper significantly.


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Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingPeople’s Republic of China

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