On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

Hongxian Zhou; Wei Xu; Shuang Li; Ying Zhang

doi:10.1016/j.amc.2007.01.052

On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

Hongxian Zhou, Wei Xu, Shuang Li, Ying Zhang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C₉¹ ⊃ [C₁¹ + 2 (C₃² ⊃ 2 C₁²)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

Original language	English
Pages (from-to)	490-499
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	190
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2007.01.052
State	Published - 1 Jul 2007

Keywords

Bifurcation
Detection functions
Hamiltonian system
Limit cycles

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10.1016/j.amc.2007.01.052

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abstract = "This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.",

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AU - Zhou, Hongxian

AU - Xu, Wei

AU - Li, Shuang

AU - Zhang, Ying

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Y1 - 2007/7/1

N2 - This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

AB - This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C91 ⊃ [C11 + 2 (C32 ⊃ 2 C12)]. These results in the paper are useful for the study of the weakened Hilbert's 16th problem.

KW - Bifurcation

KW - Detection functions

KW - Hamiltonian system

KW - Limit cycles

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JO - Applied Mathematics and Computation

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ER -

On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation

Abstract

Keywords

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