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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2018.tde-15032018-104115
Document
Author
Full name
José Hilário da Cruz
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1998
Supervisor
Committee
Táboas, Plácido Zoega (President)
Carvalho, Luiz Antonio Vieira de
Fichmann, Luiz
Garcia, Ronaldo Alves
Reis, José Geraldo dos
 
Title in Portuguese
Sobre um Problema de Perturbação Singular com Vários Retardamentos
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Consideremos a classe de equações diferenciais-diferenças singularmente perturbadas εx(t) = Σlr=0 αr x (t-r), ε > 0 (1ε e seu limite formal quando ε → 0: 0 = Σlr=0 α r x (t-r). (10). Utilizando um método introduzido por Carvalho [5], exibimos soluções periódicas de (1ε) e (10) e definimos hipersuperfícies de bifurcação dessas soluções no espaço dos parâmetros (α0, α, ...αl). Visando estabelecer relações entre as dinâmicas definidas por (1ε) e (10), no caso / = 2, α0 = 1 provamos que a região de estabilidade de (1ε) no espaço (α1, α2) aproxima a região de estabilidade de (10), quando ε → 0, num sentido definido precisamente no Teorema 4.1.1.
 
Title in English
Not available
Keywords in English
Not available
Abstract in English
We consider the class of singularly perturbed.differential-difference equations ε x(t) = Σlr=0 αr x (t-r), ε > 0 (1ε) and its formal limit as ε → 0: 0 = Σlr=0 αr x (t-r). (10). Using a method due to Carvalho [5], we exhibit periodic solutions of (1ε) and (10) and define bifurcation hypersurfaces for these solutions in the parameter space (α0, α1,...αl). Aiming to establish relations between the dynamics of (1ε) and (10) in case / = 2, α0 = 1, we prove that the stability region of (1ε) in the space (α1, α2) approaches the stability region of (10), as ε → 0, in a precise sense given in Theorem 4.1.1.
 
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JoseHilariodaCruz.pdf (5.06 Mbytes)
Publishing Date
2018-03-15
 
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