Cascade flocking with free-will

Le  Li; Lihong  Huang; Jianhong  Wu

doi:10.3934/dcdsb.2016.21.497

Article Contents

2016, Volume 21, Issue 2: 497-522. Doi: 10.3934/dcdsb.2016.21.497

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Cascade flocking with free-will

1.
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082
2.
College of Mathematics and Econometrics, Hunan University & Hunan Women's University, Changsha, Hunan, 410004
3.
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3

Received: January 31, 2015

Revised: July 31, 2015

Published: February 2016

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Abstract

We consider a self-organized system with a hierarchy structure to allow multiple leaders in the highest rank, and with free-will. In the model, we use both Cucker-Smale and Motsch-Tadmor functions for the pair influence of agents, and we derive suffcient conditions for such a system to converge to a flock, where agents ultimately move in the same velocity. We provide examples to show our suffcient conditions are sharp, and we numerically observe that such a self-organized system may have agents moving in different (final) velocities but maintain finite distance from each other due to the free-will.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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