Flocking of the Motsch–Tadmor Model with a Cut-Off Interaction Function
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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.
KeywordsMotsch–Tadmor model Cucker–Smale model Flocking Stochastic matrix Neighbor graph
Mathematics Subject Classification34A36 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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