Geodesic
Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system
Kybernetika, Tome 49 (2013) no. 6, pp. 935-947.

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In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.
Classification : 34A34, 34C05, 34C23, 34C28, 34H10, 34H20
Keywords: four-wing chaotic attractors; Lyapunov coefficient; degenerate Hopf bifurcations; period-doubling cascade 
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     author = {Liang, Hongtao and Tang, Yanxia and Li, Li and Wei, Zhouchao and Wang, Zhen},
     title = {Degenerate {Hopf} bifurcations and the formation mechanism of chaos in the {Qi} {3-D} four-wing chaotic system},
     journal = {Kybernetika},
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     zbl = {1290.34050},
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Liang, Hongtao; Tang, Yanxia; Li, Li; Wei, Zhouchao; Wang, Zhen. Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system. Kybernetika, Tome 49 (2013) no. 6, pp. 935-947. http://geodesic.mathdoc.fr/item/KYB_2013__49_6_a6/