Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays.

  title={Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays.},
  author={Jan Haskovec and Ioannis Markou},
  journal={Mathematical biosciences and engineering : MBE},
  volume={17 5},
We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions. The conditions are formulated in terms of moments of the delay distribution and they guarantee exponential decay of velocity fluctuations towards zero for large times. We demonstrate the applicability of our theory to particular delay distributions… 

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