Impact Factor

Elham Hakimi


Mazrooei-Sebdani R., Hakimi E.
Nondegenerate Hamiltonian Hopf Bifurcations in $\omega : 3 : 6$ Resonance $(\omega = 1$ or $2)$
2020, vol. 25, no. 6, pp.  522-536
This paper deals with the analysis of Hamiltonian Hopf bifurcations in threedegree-
of-freedom systems, for which the frequencies of the linearization of the corresponding
Hamiltonians are in $\omega : 3 : 6$ resonance $(\omega = 1$ or $2)$. We obtain the truncated second-order
normal form that is not integrable and expressed in terms of the invariants of the reduced
phase space. The truncated first-order normal form gives rise to an integrable system that is
analyzed using a reduction to a one-degree-of-freedom system. In this paper, some detuning
parameters are considered and nondegenerate Hamiltonian Hopf bifurcations are found. To
study Hamiltonian Hopf bifurcations, we transform the reduced Hamiltonian into standard
Keywords: Hamiltonian $\omega : 3 : 6$ resonance $(\omega = 1$ or $2)$, integrability, reduction, normal forms, Hamiltonian Hopf bifurcation
Citation: Mazrooei-Sebdani R., Hakimi E.,  Nondegenerate Hamiltonian Hopf Bifurcations in $\omega : 3 : 6$ Resonance $(\omega = 1$ or $2)$, Regular and Chaotic Dynamics, 2020, vol. 25, no. 6, pp. 522-536

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