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Master's Dissertation
DOI
10.11606/D.55.2004.tde-12012005-230105
Document
Author
Full name
Luis Roberto Almeida Gabriel Filho
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2004
Supervisor
Committee
Rodrigues, Hildebrando Munhoz (President)
Alberto, Luís Fernando Costa
Ruas Filho, Jose Gaspar
Title in Portuguese
Comportamento assintótico de sistemas não lineares discretos
Keywords in Portuguese
funções tipo Liapunov
sistemas dinâmicos
sistemas não lineares discretos
Abstract in Portuguese
Neste trabalho, apresentamos em primeiro lugar um estudo de dois trabalhos de J. P. LaSalle, abordando o comportamento assintótico de sistemas discretos. Em segundo lugar, estudamos a dinâmica de um sistema discreto que depende de um parâmetro l em L, da forma x(n+1) = f(x(n), l). Como uma parte deste objetivo geral, desenvolvemos técnicas para obter estimativas uniformes (em relação ao parâmetro l em L) do atrator quando o sistema for globalmente dissipativo. Esses métodos são baseados em funções auxiliares tipo Liapunov. No final deste trabalho, apresentamos algumas simulações envolvendo sistemas discretos caóticos, como os sistemas de Chua, Hénon, Ikeda, Lorenz e Rössler.
Title in English
Asymptotic behavior of non lineal discrete systems
Keywords in English
discrete non lineal systems
dynamics system
functions of Liapunov type
Abstract in English
Firstly, in this work, we present a study of part of two works by J. P. LaSalle, concerning with asymptotic behavior of discrete systems. Secondly, we study the dynamics of a discrete system that depends on a parameter l in L, of the form x(n+1) = f(x(n), l). As part of this general purpose, we develop tecniques to obtain uniform estimates (with respect to the parameter l in L) of the attractor when the system is globally dissipative. These methods are based on auxiliary functions of Liapunov type. In the last part of this work we present some simulations envolving chaotic discrete systems, namely: Chua, Hénon, Ikeda, Lorenz and Rössler.
 
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Dissertacao.pdf (2.10 Mbytes)
Publishing Date
2005-01-18
 
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