Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (3): 45-51.doi: 10.16088/j.issn.1001-6600.2020.03.006
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ZHANG Erli1*, XING Yuqing2
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| [1] LI C Z, LLIBRE J, ZHANG Z F. Weak focus, limit cycles and bifurcations for bounded quadratic systems[J].Journal of Differential Equations, 1995,115: 193-223.DOI: 10.1006/jdeq.1995.1012. [2] GIACOMINI H, LLIBRE J. On the shape of limit cycles that bifurcate from non-Hamiltonian center[J].Nonlinear Analysis, 2001,43: 837-859.DOI: 10.1016/S0362-546X(98)00294-6. [3] GINÉJ, LLIBRE J. Limit cycles of cubic polynomial vector fields via the averaging theory[J].Nonlinear Analysis, 2007,66: 1707-1721.DOI: 10.1016/j.na.2006.02.016. [4] ATABAIGI A, NYAMORADI N, ZANGENEH H R. The number of limit cycles of a quintic polynomial system with center[J].Nonlinear Analysis, 2009,71: 3008-3017.DOI: 10.1016/j.na.2009.01.213. [5] HAN M A, ROMANOVSKI G, ZHANG X. Equivalence of the Melnikov function method and the averaging method[J].Qualitative Theory of Dynamical Systems, 2016,15: 471-479.DOI: 10.1007/s12346-015-0179-3. [6] BUICÂ A, LLIBRE J. Averaging methods for finding periodic orbits via Brouwer degree[J].Bulletin Des Sciences Mathematiques, 2004,128: 7-22.DOI: 10.1016/j.bulsci.2003.09.002. [7] 朱科科. 一类三次系统极限环的存在性[J].安阳师范学院学报,2017(5):4-8.DOI: 10.16140/j.cnki.1671-5330.2017.05.002. [8] 袁丽萍. 带两个区域的平面分段光滑系统的非双曲极限环分岔[J].四川大学学报(自然科学版),2018,55(4): 678-682.DOI: 10.3969/j.issn.0490-6756.2018.04.004. [9] 占家佳, 黄文韬, 何东平. 一类四次Kolmogorov系统的中心与极限环[J].桂林电子科技大学学报,2018,38(3): 242-246.DOI: 10.16725/j.cnki.cn45-1351/tn.2018.03.015. [10]WANG H, LIANG F. Limit cycles by perturbing a piecewise near-Hamiltonian system with 4 switching lines[J].Mathematica Applicata,2019,32(4): 832-837.DOI: 10.13642/j.cnki.42-1184/o1.2019.04.059. [11]王彬瑶, 李宝毅, 张永康. 一类分段线性Hamilton系统在多项式扰动下极限环个数的下界[J].天津师范大学学报(自然科学版), 2018,38(5):10-14. DOI: 10.19638/j.issn1671-1114.20180502. [12]杨纪华, 尚华辉. 一类三次Hamiltonian系统Abelian积分的零点个数估计[J].黑龙江大学自然科学学报, 2017,34(3): 291-296.DOI: 10.13482/j.issn1001-7011.2016.06.226. [13]LLIBRE J, DEL RIO J S, RODRIGUEZ J A. Averaging analysis of a perturbated quadratic center[J].Nonlinear Analysis, 2001,46: 45-51.DOI: 10.1016/S0362-546X(99)00444-7. [14]BUICÂ A, LLIBRE J. Limit cycles of a perturbed cubic polynomial differential center[J].Chaos Solitons and Fractals, 2007,32: 1059-1069.DOI: 10.1016/j.chaos.2005.11.060. [15]COLL B, LLIBRE J, PROHENS R. Limit cycles bifurcating from a perturbed quartic center[J].Chaos Solitons and Fractals,2011,44: 317-334.DOI: 10.1016/j.chaos.2011.02.009. [16]LI S M, ZHAO Y L, LI J. On the number of limit cycles of a perturbed cubic polynomial differential center[J].Journal of Mathematical Analysis and Applications, 2013,404:212-220.DOI: 10.1016/j.jmaa.2013.03.010. [17]LLIBRE J, NOVAES D, TEIXEIRA M. On the birth of limit cycles for non-smooth dynamical systems[J].Bulletin Des Sciences Mathematiques, 2014,139: 229-244.DOI: 10.1016/j.bulsci.2014.08.011. [18]YANG J, ZHAO L. Limit cycle bifurcations for piecewise smooth integrable differential systems[J].Discrete and Continuous Dynamical Systems Series B,2017,22: 2417-2425.DOI: 10.3934/dcdsb.2017123. |
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