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|Title: ||Hierarchical leadership and collision avoidance in flocking|
|Other Titles: ||Flocking mo xing zhong de deng ji zhi du he peng zhuang bi mian|
|Authors: ||Dong, Jiugang ( 董久刚)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2011|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Numerical analysis.|
|Notes: ||CityU Call Number: QA297 .D66 2011|
v, 66 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2011.
Includes bibliographical references (leaves -66)
|Abstract: ||Flocking is a phenomenon in which a number of interacting agents, using only limited
information and simple rules, organize into an ordered motion without a central direction.
In recent years, this phenomenon has attracted more and more attention from
researchers in biology, physics, robotics, control theory and computer science. Recently,
a flocking model was introduced by Cucker and Smale together with a result
establishing the convergence to flocking depending on initial conditions and system parameters.
This thesis investigates some problems related to the Cucker-Smale model.
The main contributions of the thesis can be summarized as follows.
The chapter 2 of the thesis considers the Cucker-Smale model under hierarchical
leadership. For the original Cucker-Smale model, Cucker and Smale established unconditional
convergence to a common velocity provided the interaction between the
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 the
unconditional convergence stops holding is β = 1/2. The Cucker-Smale 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 β < 1/2k (k being the number of agents). In this chapter
we improve this result by showing that unconditional convergence holds indeed for
β < 1/2.
The chapter 3 of the thesis considers the Cucker-Smale model with collision avoid ance. We extend the Cucker-Smale model by adding to it a repelling force between
agents and show that, for this modified model, convergence to flocking is established
while, in addition, avoidance of collisions (i.e., the respect of a minimal distance between
agents) is ensured.
The chapter 4 of the thesis proves a general result of collision-avoiding flocking.
The underlying model allows several forms of coupling forces and the main result
ensures collision-avoiding flocking provided the initial state of the population does
not show simultaneously very different velocities, very spread positions or very close
The results of this thesis have already been published (or accepted for publication)
in academic journals. Thus, the contents in Chapter 2 appear in , those of Chapter 3
in , and those of Chapter 4 are to appear in .|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b4086780|
|Appears in Collections:||MA - Doctor of Philosophy |
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