Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
نویسندگان
چکیده
This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. By employing the detection function method for global bifurcations of limit cycles and the normal form theory for local degenerate Hopf bifurcations, 31 and 35 limit cycles and their configurations are obtained for different sets of controlled parameters. It is shown that: H(6) P 35 = 6 1, where H(6) is the Hilbert number for sixth-degree polynomial systems. 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
An Improved Lower Bound on the Number of Limit Cycles Bifurcating from a quintic Hamiltonian Planar Vector Field under quintic Perturbation
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