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Doctoral Thesis
DOI
Document
Author
Full name
Sandra Maria Semensato de Godoy
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1989
Supervisor
Committee
Reis, José Geraldo dos (President)
Bassanezi, Rodney Carlos
Claeyssen, Julio Cesar Ruiz
Nowosad, Pedro
Táboas, Plácido Zoega
Title in Portuguese
EXISTÊNCIA DE SOLUÇÕES PERIÓDICAS, ESTABILIDADE E APLICAÇÕES DE UMA CLASSE DE EQUAÇÕES DIFERENCIAIS RETARDADAS AUTÔNOMAS NÃO LINEARES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Não disponível
Title in English
Not available
Keywords in English
Not available
Abstract in English
The retarded differential equation (I) x(t) = λx(t) + λF(x(t-1)), was studied. First, some applications on three biological models were mad. It was shown that for λ going to infinity, under mild conditions in F : R → R, i. e., F has stable orbit 2-periodic, the periodic solutions of (I), converge to "square wave" type function. Sequentially, studing the stability of the solutions, for F : Rn → Rn, it was shown that it only depends on the eigenvalues DF(0). Finally, applying additional hypothesis in F, it was shown the existence of periodical for λ > λ0, being DF(0) a rotation folowed by a stretching, i.e. , the Jacobian matriz of DF(0) assumes one of the following forms: [ a b] / [-b a] or [a -b] / [b a], a > 0, b > 0, b > a, a2 + b2 > 1.
 
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Publishing Date
2019-10-30
 
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