# American Institute of Mathematical Sciences

October  2016, 21(8): 2587-2599. doi: 10.3934/dcdsb.2016062

## A new discrete Cucker-Smale flocking model under hierarchical leadership

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

Received  July 2015 Revised  May 2016 Published  September 2016

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.
Citation: Chun-Hsien Li, Suh-Yuh Yang. A new discrete Cucker-Smale flocking model under hierarchical leadership. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2587-2599. doi: 10.3934/dcdsb.2016062
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