A new discrete Cucker-Smale flocking model under hierarchical leadership

Chun-Hsien  Li; Suh-Yuh  Yang

doi:10.3934/dcdsb.2016062

Article Contents

2016, Volume 21, Issue 8: 2587-2599. Doi: 10.3934/dcdsb.2016062

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A new discrete Cucker-Smale flocking model under hierarchical leadership

Chun-Hsien Li^1, and
Suh-Yuh Yang^2,

1.
Department of Mathematics, National Kaohsiung Normal University, Yanchao District, Kaohsiung City 82444
2.
Department of Mathematics, National Central University, Jhongli District, Taoyuan City 32001

Received: June 30, 2015

Revised: April 30, 2016

Published: September 2016

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Abstract

This paper studies the flocking behavior in a new discrete-time Cucker-Smale model under hierarchical leadership. The features of this model are that each individual has its own intrinsic nonlinear dynamics and the interaction between individuals follows a hierarchical leadership structure. Based on a specific matrix norm, we prove that the conditional flocking indeed occurs. Numerical experiments are given to confirm the theoretical results.

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Mathematics Subject Classification: Primary: 92D25, 92D50; Secondary: 92B25, 93C55.

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References

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