Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

Hongxian Zhou; Wei Xu

doi:10.1016/j.amc.2008.02.042

Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

Hongxian Zhou, Wei Xu

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

Abstract

The number and distribution of limit cycles of a cubic Hamiltonian system under higher-order perturbed terms is investigated. By using the bifurcation theory and the method of detection function, we obtain that there exist at least 13 limit cycles with the distribution C₇¹ ⊃ 2 [C₃² ⊃ 2 C₁²] in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.

Original language	English
Pages (from-to)	905-913
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	204
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2008.02.042
State	Published - 15 Oct 2008

Keywords

Abelian integrals
Bifurcation
Detection functions
Hamiltonian system
Limit cycle

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10.1016/j.amc.2008.02.042

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abstract = "The number and distribution of limit cycles of a cubic Hamiltonian system under higher-order perturbed terms is investigated. By using the bifurcation theory and the method of detection function, we obtain that there exist at least 13 limit cycles with the distribution C71 ⊃ 2 [C32 ⊃ 2 C12] in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.",

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AU - Xu, Wei

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N2 - The number and distribution of limit cycles of a cubic Hamiltonian system under higher-order perturbed terms is investigated. By using the bifurcation theory and the method of detection function, we obtain that there exist at least 13 limit cycles with the distribution C71 ⊃ 2 [C32 ⊃ 2 C12] in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.

AB - The number and distribution of limit cycles of a cubic Hamiltonian system under higher-order perturbed terms is investigated. By using the bifurcation theory and the method of detection function, we obtain that there exist at least 13 limit cycles with the distribution C71 ⊃ 2 [C32 ⊃ 2 C12] in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.

KW - Abelian integrals

KW - Bifurcation

KW - Detection functions

KW - Hamiltonian system

KW - Limit cycle

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M3 - 文章

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SN - 0096-3003

VL - 204

SP - 905

EP - 913

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

Abstract

Keywords

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