@PhDThesis{Ferreira:2014:DeSiFa,
author = "Ferreira, Maria Teodora",
title = "Detec{\c{c}}{\~a}o da sincroniza{\c{c}}{\~a}o de fase em
sistemas ca{\'o}ticos por meio da transformada wavelet complexa
dual–tree",
school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
year = "2014",
address = "S{\~a}o Jos{\'e} dos Campos",
month = "2014-06-24",
keywords = "sincroniza{\c{c}}{\~a}o de fase, transformada wavelet complexa
dual-tree, sistemas ca{\'o}ticos, an{\'a}lise de s{\'e}ries
temporais, phase synchronization, dual-tree complex wavelet
transform, chaotic systems, time series analysis.",
abstract = "Neste trabalho {\'e} proposto um novo m{\'e}todo para calcular a
fase de sistemas ca{\'o}ticos e de conjuntos de dados
experimentais, a fim de analisar o fen{\^o}meno de
sincroniza{\c{c}}{\~a}o de fase. A sincroniza{\c{c}}{\~a}o de
fase ocorre, principalmente, quando se tem um acoplamento fraco
entre os sistemas ocasionando um travamento na fase enquanto as
amplitudes permanecem n{\~a}o correlacionadas. O m{\'e}todo
proposto, denominado \emph{wavelet dt-cwt}, {\'e} baseado na
utiliza{\c{c}}{\~a}o da transformada \emph{wavelet} discreta
complexa \emph{dual-tree}, a qual {\'e} uma transformada
\emph{wavelet} complexa quase-ortogonal, com algoritmos
r{\'a}pidos, possui boa invari{\^a}ncia a deslocamentos e
redund{\^a}ncia limitada. A aplicabilidade do m{\'e}todo
\emph{wavelet dt-cwt} {\'e} testada em: cinco diferentes
experimentos envolvendo o sistema de R{\~o}ssler; dois
experimentos envolvendo o sistema de Lorenz; no Modelo de Kuramoto
imerso no Plano e na Faixa de M{\'o}ebius e, em quatro diferentes
conjuntos de dados experimentais. Os resultados obtidos com o
m{\'e}todo mostram-se eficientes em rela{\c{c}}{\~a}o aos
m{\'e}todos j{\'a} existentes para este fim, devido a seu baixo
custo computacional, da ordem de \emph{2N} com N sendo o
n{\'u}mero de pontos da s{\'e}rie temporal, quando comparado com
a transformada \emph{wavelet} cont{\'{\i}}nua, a qual apresenta
um custo da ordem de \$N^{2}\$. A efici{\^e}ncia do m{\'e}todo
proposto tamb{\'e}m se destaca no fato do mesmo n{\~a}o exigir a
reconstru{\c{c}}{\~a}o do atrator no espa{\c{c}}o de estado,
sendo que, {\'e} suficiente apenas uma vari{\'a}vel de cada
sistema em estudo ou a s{\'e}rie temporal experimental; devido a
possibilidade de ser aplicado em s{\'e}ries temporais com grande
n{\'u}mero de pontos; o fato de ser robusto a moderados
n{\'{\i}}veis de ru{\'{\i}}do aditivo e sua
localiza{\c{c}}{\~a}o acurada nas mudan{\c{c}}as de fase.
ABSTRACT: In this work, it is proposed a method to calculate the
phase of chaotic systems and of sets of experimental data in arder
to analyze the phenomenon of phase synchronization. The phase
synchronization mainly occurs when there is a coupling weak
between the systems causing a locking in the phases while the
amplitudes remain uncorrelated. The proposed method,called wavelet
dt-cwt, is based on the use of dual-tree complex wavelet
transform, which is a quasi-orthogonal complex wavelet transform,
with fast algarithms, has good invariance to shifts and limited
redundancy. The applicability of the \emph{wavelet dt-cwt} method
is tested in: five different experiments involving the system of
R{\^o}ssler: two experiments involving the Lorenz system; the
Kuramoto model immersed in the Plan and the Moebius Strip and with
and without noise, and four different sets of experimental data.
The results show the method is efficient compared with existing
methods for this purpose, due to its low computational cost - on
the order of 2N with N being the number of points in the time
series - when compared with the continuous wavelet transform,
which presents a cost the order of \$N^{2}\$. The efficiency of
the proposed method also stands out in the fact that the same does
not require the reconstruction of the attractor in the state
space, being that, is sufficient a single variable of each system
under study or experimental time series; due to the possibility of
being applied in series with a large number of points; the fact
that it is robust to moderate leveis of additive noise and its
accurate location on the phase changes.",
committee = "Quiles, Marcos Gon{\c{c}}alves (presidente) and Macau, Elbert
Einstein Nehrer (orientador) and Domingues, Margarete Oliveira
(orientador) and Castro, Joaquim Jos{\'e} Barroso de and
Carvalho, Ricardo Egydio de and Viana, Ricardo Luiz",
englishtitle = "Detecting phase synchronization in chaotic systems by dual-tree
complex wavelet transform",
language = "pt",
pages = "202",
ibi = "8JMKD3MGP5W34M/3GESL58",
url = "http://urlib.net/ibi/8JMKD3MGP5W34M/3GESL58",
targetfile = "publicacao.pdf",
urlaccessdate = "03 jun. 2024"
}