0
2013
Impact Factor

Reza Mazrooei-Sebdani

Isfahan University of Technology

Publications:

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
Abstract
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
form.
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
DOI:10.1134/S1560354720060027

Back to the list