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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. (English) Zbl 1290.34050

Kybernetika 49, No. 6, 935-947 (2013).
Summary: 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 a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

four-wing chaotic attractors; Lyapunov coefficient; degenerate Hopf bifurcations; period-doubling cascade
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\textit{H. Liang} et al., Kybernetika 49, No. 6, 935--947 (2013; Zbl 1290.34050)
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