Equações Diferenciais não Lineares com Três Retardos: Estudo Detalhado das Soluções

Figueiredo, Júlio César Bastos de

doi:10.11606/T.43.2000.tde-28112013-102436

Início

Servicios

Tesis Doctoral

DOI

https://doi.org/10.11606/T.43.2000.tde-28112013-102436

Documento

Tesis Doctoral

Autor

Figueiredo, Júlio César Bastos de (Catálogo USP)

Nombre completo

Júlio César Bastos de Figueiredo

Instituto/Escuela/Facultad

Instituto de Física

Área de Conocimiento

Física Nuclear

Fecha de Defensa

2000-05-25

Publicación

São Paulo, 2000

Director

Malta, Coraci Pereira (Catálogo USP)

Tribunal

Malta, Coraci Pereira (Presidente)
Caldas, Ibere Luiz
Furuie, Sergio Shiguemi
Koiller, Jair
Ranvaud, Ronald Dennis Paul Kenneth Clive

Título en portugués

Equações Diferenciais não Lineares com Três Retardos: Estudo Detalhado das Soluções

Palabras clave en portugués

Equações diferenciais não lineares
Física teórica

Resumen en portugués

In this thesis we study the behavior of a simple control system based on a delay differential equation with multiple loops of negative feedback. Numerical solutions of the delay differential equation with N delays d/dt x(t) = -x(t) + 1/N POT.N IND.i=1 / POT.n IND.i + x (t- IND.i) POT.n have been investigated as function of its parameters: n, i and i. A simple numerical method for determine the stability regions of the equilibrium points in the parameter space (i, n) is presented. The existence of a doubling period route to chaos in the equation, for N = 3, is characterized by the construction of bifurcation diagram with parameter n. A numerical method that uses the analysis of Poincaré sections of the reconstructed attractor to find aperiodic solutions in the parameter space of the equation is also presented. We apply this method for N = 2 and get evidences for the existence of chaotic solutions as result of a period doubling route to chaos (chaotic solutions for N = 2 in that equation had never been observed). Finally, we study the solutions of a piecewise constant equation that corresponds to the limit case n .

Título en inglés

Nonlinear differential equations with three delays: detailed study of the solutions.

Palabras clave en inglés

Nonlinear differential equations
Theoretical physics

Resumen en inglés

In this thesis we study the behavior of a simple control system based on a delay differential equation with multiple loops of negative feedback. Numerical solutions of the delay differential equation with N delays d/dt x(t) = -x(t) + 1/N POT.N IND.i=1 / POT.n IND.i + x (t- IND.i) POT.n have been investigated as function of its parameters: n, i and i. A simple numerical method for determine the stability regions of the equilibrium points in the parameter space (i, n) is presented. The existence of a doubling period route to chaos in the equation, for N = 3, is characterized by the construction of bifurcation diagram with parameter n. A numerical method that uses the analysis of Poincaré sections of the reconstructed attractor to find aperiodic solutions in the parameter space of the equation is also presented. We apply this method for N = 2 and get evidences for the existence of chaotic solutions as result of a period doubling route to chaos (chaotic solutions for N = 2 in that equation had never been observed). Finally, we study the solutions of a piecewise constant equation that corresponds to the limit case n .

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Fecha de Publicación

2013-12-18

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