Geodesic
Hopf bifurcations and small amplitude limit cycles in Rucklidge systems
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 34A34, 34D20, 34C07
Keywords: rucklidge system, limit cycle, stability, Lyapunov coefficient 
@article{EJDE_2013__2013__a3,
     author = {Dias,  Fabio Scalco and Mello,  Luis Fernando},
     title = {Hopf bifurcations and small amplitude limit cycles in {Rucklidge} systems},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1290.34045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a3/}
}
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AU  - Mello,  Luis Fernando
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JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
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%A Dias,  Fabio Scalco
%A Mello,  Luis Fernando
%T Hopf bifurcations and small amplitude limit cycles in Rucklidge systems
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a3/
%G en
%F EJDE_2013__2013__a3
Dias,  Fabio Scalco; Mello,  Luis Fernando. Hopf bifurcations and small amplitude limit cycles in Rucklidge systems. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a3/