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|Title: ||Synchronization analysis of polytopic complex dynamical network|
|Other Titles: ||Ju you tu zu he xing zhi de fu za dong tai wang luo de tong bu xing fen xi|
|Authors: ||Huang, Chi (黃遲)|
|Department: ||Department of Mathematics|
|Degree: ||Master of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||System analysis -- Mathematical models.|
|Notes: ||CityU Call Number: QA402 .H825 2009|
vii, 77 leaves 30 cm.
Thesis (M.Phil.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves -77)
|Abstract: ||Complex dynamical networks are ubiquitous in our real world, ranging from biological,
physical, to social networks. Over the past decade, much of the interesting dynamical
behaviour of complex dynamical networks, such as synchronization, spatiotemporal
chaos, auto-waves and spiral waves, has recently attracted increasing attention
from researchers in different areas. Among these, synchronization has been a hot
research topic in recent years. Synchronization behaviour of networks is a universal
phenomenon in nature; while, synchronization techniques have been widely applied in
our daily life. Hence, there is a great demand to study synchronization behaviour of
complex dynamical networks.
There are some common phenomena in most real-world networks including the diversity
of complex networks, structural uncertainty and time-varying links. Research
on the corresponding concerned issues of synchronization analysis of complex dynamical
networks will be presented in this thesis. The research problems are as follows:
(a) Is it possible to establish synchronization criteria of a group of complex networks?
(b) How does one establish synchronization criteria of complex networks with structural
uncertainty? (c) How does one propose synchronization criteria of time-varying
Problem (a) arises from the fact that in practice people always have to investigate
the synchronization of many different networks. The existing results can check
the synchronization behaviour for only one complex network, which motivates the research
of Problem (a). In this thesis, the concept of the polytopic complex network
family is first defined. The models of inner and outer network families are constructed.
The coupling delay, a common phenomenon of real life networks, is also considered in these models. The delay independent and delay dependent synchronization criteria
are derived for inner and outer network families, respectively. Compared with the existing
results, the proposed synchronization criteria in this thesis are satisfied by a set
of complex networks within the same family, rather than being applied for only single
Since intrinsic physical disturbances exist in real-life networks, the structural uncertainty
of complex networks is unavoidable. Thus, Problem (b) arises, which few
results have addressed. In this thesis, some sufficient conditions to guarantee the synchronization
of complex networks with structural uncertainty will be derived. The
uncertainty is considered in inner and outer coupling matrices of complex networks,
which represent the network structure. Both polytopic and norm-bounded representations
of uncertainty are discussed in detail.
It is widely known that many real networks have time-varying structure. Hence,
Problem (c) is investigated. In this thesis, the time-varying polytopic complex network
is constructed. Based on the parameter-dependent Lyapunov function, the global
synchronization criterion is proposed. In our result, the condition on the negative definition
of some time-varying matrices has been removed, thus providing a more convenient
way to verify the condition when compared with existing results.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b3947870|
|Appears in Collections:||MA - Master of Philosophy |
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