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Doctoral Thesis
DOI
10.11606/T.3.2017.tde-31032017-082016
Document
Author
Full name
José Roberto Castilho Piqueira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1987
Supervisor
Title in Portuguese
Aplicação da teoria qualitativa de equações diferenciais a problemas de sineronismo de fase
Keywords in Portuguese
Bifurcações
Caos
Dinâmica
Equações diferenciais (Aplicações)
Sincronismo
Abstract in Portuguese

Aplica-se a Teoria Qualitativa de Equações Diferenciais aos problemas de sincronismo de fase, associando às diversas regiões do espaço de parâmetros os tipos de atratores esperados.

Três casos básicos são estudados:

  1. Malha de Sincronismo de fase Autônoma de 2ª Ordem
  2. Modulação em Frequência Acidental em Malha de Sincronismo de Fase de 2ª Ordem
  3. Malha de Sincronismo de Fase Autônoma de 3ª Ordem

No caso (i), usando resultados clássicos da teoria de sistemas dinâmicos, discute-se os pontos de equilíbrio e os ciclos limite.

No caso (ii), usando o método de Melnikov propõem-se critérios para previsão de aparecimento de atratores caóticos.

No caso (iii), usando o teorema de bifurcações de Hopf, a estabilidade dos pontos de equilíbrio e a formação dos ciclos limite são analisadas

Title in English
Qualitative theory of differential equations applied to phase synchronism problems.
Keywords in English
Bifurcations
Chaos
Dynamics
Synchronism
Abstract in English

The Qualitative Theory of Differential Equations is applied to the phaselock problems, and the several parameters space regions are associated to the expected attractors.

Three basic cases are studied:

  1. Autonomous Second Order Phaselock Loop
  2. Accidental Frequency Modulation on Second Orer Phaselock Loop
  3. Autonomous Third Order Phaselock Loop

In case i), using classical results of dynamical systems theory, the equilibrium points and limit cycles are analyses.

In case ii), the Melnikov technique gives some criteria for chaotic attractors.

In case iii), Hopf bifurcation theorem provides propositions about equilibrium points and limit cycles.

 
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Publishing Date
2017-03-31
 
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