Fabio Scalco Dias, Luis Fernando Mello
Abstract:
In this article we study Hopf bifurcations and small amplitude limit
cycles in a family of quadratic systems in the three dimensional
space called Rucklidge systems.
Bifurcation analysis at the equilibria of Rucklidge system is pushed
forward toward the calculation of the second Lyapunov coefficient,
which makes possible the determination of the Lyapunov and higher
order structural stability.
Submitted February 7, 2012. Published February 12, 2013.
Math Subject Classifications: 34A34, 34D20, 34C07.
Key Words: Rucklidge system; limit cycle; stability; Lyapunov coefficient.
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Fabio Scalco Dias Instituto de Matemática e Estatística, Universidade Federal de Itajubá Avenida BPS 1303, Pinheirinho CEP 37.500--903, Itajubá, MG, Brazil email: scalco@unifei.edu.br |
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Luis Fernando Mello Instituto de Matemática e Estatística, Universidade Federal de Itajubá Avenida BPS 1303, Pinheirinho CEP 37.500--903, Itajubá, MG, Brazil email: lfmelo@unifei.edu.br |
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