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

@article{Haskovec2020ExponentialAF, 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}, year={2020}, volume={17 5}, pages={ 5651-5671 } }

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…

## 6 Citations

Cucker-Smale model with finite speed of information propagation: well-posedness, flocking and mean-field limit

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We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed c > 0. This leads to a system of functional differential equations with state-dependent…

The delayed Cucker-Smale model with short range communication weights

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A simple sufficient condition of the initial data to the non-flocking behavior of the delayed Cucker-Smale model is established and a flocking result is obtained, which also depends upon theinitial data in the short range communication case.

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We study the invariance of velocity angles and flocking properties of the Inertial Spin model introduced by Cavagna et al. [J. Stat. Phys., 158, (2015), 601–627]. We present a novel approach, based…

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We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consider both the…

Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

Non-flocking and flocking for the Cucker-Smale model with distributed time delays

- Journal of the Franklin Institute
- 2022

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