@article{21230db5100542c9a8c0eb2e73fc7835, title = "On the critical exponent for flocks under hierarchical leadership", abstract = "Very recently, a model for flocking was introduced by Cucker and Smale together with a proof of convergence. This proof established unconditional convergence to a common velocity provided the interaction between agents was strong enough and conditional convergence otherwise. The strength of the interaction is measured by a parameter β <0 and the critical value at which unconditional convergence stops holding is β = 1/2. This model was extended by Shen to allow for a hierarchical leadership structure among the agents and similar convergence results were proved. But, for discrete time, unconditional convergence was proved only for $\beta <\frac{1}{2k}$ (k being the number of agents). In this note we improve on this result showing that unconditional convergence holds indeed for β <1/2. {\textcopyright} 2009 World Scientific Publishing Company.", keywords = "Hierarchical leadership, Unconditional convergence.", author = "Felipe Cucker and Jiu-Gang Dong", year = "2009", month = aug, doi = "10.1142/S0218202509003851", language = "English", volume = "19", pages = "1391--1404", journal = "Mathematical Models and Methods in Applied Sciences", issn = "0218-2025", publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD", number = "SUPPL. 1", }