Limit cycles in a quartic system with a third-order nilpotent singular point

被引：1

作者：

Li, Xinli ^{[1
,2
]}

机构：

[1] Univ Shanghai Sci & Technol, Sch Business, Shanghai, Peoples R China

[2] Linyi Univ, Logist Sch, Linyi, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

关键词：

Quartic system; Nilpotent critical point; Lyapunov constants; Bifurcation of limit cycles; LYAPUNOV SYSTEM; HAMILTONIAN-SYSTEMS; BIFURCATIONS; CENTERS;

D O I：

10.1186/s13662-018-1607-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, limit cycles bifurcating from a third-order nilpotent critical point in a class of quartic planar systems are studied. With the aid of computer algebra system MAPLE, the first 12 Lyapunov constants are deduced by the normal form method. As a result, sufficient and necessary center conditions are derived, and the fact that there exist 12 or 13 limit cycles bifurcating from the nilpotent critical point is proved by different perturbations. The result in [Qiu et al. in Adv. Differ. Equ. 2015(1):1, 2015] is improved.

引用

页数：15

共 50 条

[1] Limit cycles in a quartic system with a third-order nilpotent singular point
Xinli Li
[J]. Advances in Difference Equations, 2018
[2] Third-order bifurcation of limit cycles for a perturbed quartic isochronous centre
Huang, Bo
Peng, Linping
[J]. INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2023, 13 (03) : 165 - 182
[3] LIMIT CYCLES OF THIRD-ORDER DIFFERENTIAL EQUATION
Amar Makhlouf
Meriem Hamamda
[J]. Annals of Applied Mathematics, 2014, 30 (04) : 416 - 423
[4] Bifurcation of limit cycles for a class of cubic polynomial system having a nilpotent singular point
Pan, Xuejun
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) : 1161 - 1165
[5] LIMIT CYCLES FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS
Llibre, Jaume
Yu, Jiang
Zhang, Xiang
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (02) : 581 - 594
[6] Bifurcation of Limit Cycles for Some Lienard Systems with a Nilpotent Singular Point
Yang, Junmin
Sun, Xianbo
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (05):
[7] On the number of limit cycles near a homoclinic loop with a nilpotent singular point
An, Yulian
Han, Maoan
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (09) : 3194 - 3247
[8] Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point
Li, Feng
Li, Shimin
[J]. NONLINEAR DYNAMICS, 2019, 96 (01) : 553 - 563
[9] Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point
Feng Li
Shimin Li
[J]. Nonlinear Dynamics, 2019, 96 : 553 - 563
[10] Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center
Yang, Junmin
Yu, Pei
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 298 : 141 - 152

← 1 2 3 4 5 →