Mecanismos de Criação de Atratores Estranhos no Segundo Sistema de Rössler
DOI:
https://doi.org/10.5540/tema.2008.09.02.0275Abstract
Neste trabalho fazemos uma análise das bifurcações locais que ocorrem nos pontos de equilíbrio do Segundo Sistema de Rössler, que é um sistema quadrático tridimensional de equações diferenciais ordinárias, dependendo de três parâmetros reais, a, b e c. Determinamos as superfícies no espaço de parâmetros, para as quais o sistema apresenta bifurcações de Hopf. Mostramos numericamente que para valores dos parâmetros próximos aos de bifurcação de Hopf o sistema possui atratores estranhos. Além disso, para a = 0 o sistema possui uma família formada por infinitos ciclos heteroclínicos singularmente degenerados, que consistem de conjuntos invariantes formados por uma linha de equilíbrios, juntamente com uma órbita heteroclínica conectando dois destes equilíbrios. Mostramos numericamente que pequenas perturbações do sistema, tomando-se a > 0 pequeno,levam à quebra destes ciclos degenerados e à criação de atratores estranhos.References
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