LIAPUNOV CONSTANTS AND HOPF CYCLICITYOF LIENARD SYSTEMS 被引量：8

LIAPUNOV CONSTANTS AND HOPF CYCLICITY OF LIENARD SYSTEMS

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摘要 We establish an algebraic method and an integral method to compute the Liapunov constants and Hopf cyclicity for a general Lienard system on the plane. We establish an algebraic method and an integral method to compute the Liapunov constants and Hopf cyclicity for a general Lienard system on the plane.

作者韩茂安

出处《Annals of Differential Equations》 1999年第2期113-126,共14页 微分方程年刊（英文版）

关键词 Hopf cyclicity limit cycle Liapunov constant Hopf cyclicity, limit cycle, Liapunov constant

分类号 O175 [理学—数学]

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同被引文献10

1韩茂安.Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems[J].Science China Mathematics,1994,37(11):1325-1336. 被引量：7
2Yang Junmin Han Maoan (Dept.of Math.,Shanghai Normal University,Shanghai 200234).LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP[J].Annals of Differential Equations,2007,23(4):536-545. 被引量：2
3韩茂安.中心与焦点判定定理证明之补充[J].大学数学,2011,27(1):142-147. 被引量：4
4韩茂安,陈健.On the number of limit cycles in double homoclinic bifurcations[J].Science China Mathematics,2000,43(9):914-928. 被引量：16
5韩茂安,叶彦谦.ON THE COEFFICIENTS APPEARING IN THE EXPANSION OF MELNIKOV FUNCTIONS IN HOMOCLINIC BIFURCATIONS[J].Annals of Differential Equations,1998,14(2):58-64. 被引量：4
6HAN MaoAn,TIAN Yun,YU Pei.Small-amplitude limit cycles of polynomial Linard systems[J].Science China Mathematics,2013,56(8):1543-1556. 被引量：3
7韩茂安.平面系统中心与焦点判定问题的若干注释[J].上海师范大学学报（自然科学版）,2013,42(6):565-579. 被引量：2
8韩茂安.牛顿-莱布尼兹公式与泰勒公式的拓展与应用[J].大学数学,2015,31(5):6-11. 被引量：5
9盛丽鹃,韩茂安.一维周期方程的周期解问题[J].中国科学：数学,2017,47(1):171-186. 被引量：4
10Mao An HAN,Xia Yu ZHOU.On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems[J].Acta Mathematica Sinica,English Series,2024,40(7):1785-1803. 被引量：1

引证文献8

1Yun Tian, Yepeng Xing (Dept. of Math., Shanghai Normal University, Shanghai 200234).ON THE NUMBER OF LIMIT CYCLES OF A CUBIC SYSTEM NEAR A CUSPIDAL LOOP[J].Annals of Differential Equations,2010,26(2):222-226.
2严冬梅,田云.一类Lienard系统的Hopf环形数(英文)[J].浙江大学学报（理学版）,2011,38(1):10-18.
3HAN MaoAn,TIAN Yun,YU Pei.Small-amplitude limit cycles of polynomial Linard systems[J].Science China Mathematics,2013,56(8):1543-1556. 被引量：3
4高玉景.一类带有强Allee效应捕食-食饵系统的Hopf分支[J].兰州大学学报（自然科学版）,2014,50(4):564-568. 被引量：3
5梁峰,李洁,鲁世平.具非初等焦点的分段光滑Liénard系统的极限环分支(英文)[J].四川大学学报（自然科学版）,2015,52(6):1192-1198.
6苗稼乐,杨俊敏.Melnikov函数在含有两个幂零尖点的双异宿环附近的展开式[J].上海师范大学学报（自然科学版）,2020,49(3):295-310.
7Junmin Yang,Maoan Han.Some properties of Melnikov functions near a cuspidal loop[J].Science China Mathematics,2024,67(4):767-786.
8韩茂安.平面系统的Hopf分支理论[J].四川师范大学学报（自然科学版）,2024,47(6):738-752.

二级引证文献6

1汪维刚,史娟荣,莫嘉琪.捕食-被捕食微分方程种群模型的研究综述[J].武汉大学学报（理学版）,2015,61(4):299-307. 被引量：7
2梁峰,李洁,鲁世平.具非初等焦点的分段光滑Liénard系统的极限环分支(英文)[J].四川大学学报（自然科学版）,2015,52(6):1192-1198.
3蒋芮,刘华,谢梅,魏玉梅,赵仕凤.具有HollingⅡ型功能反应和Allee效应的捕食系统模型[J].高校应用数学学报（A辑）,2016,31(4):441-450. 被引量：4
4蔡琴.全方位移动避障实时轨迹控制算法的研究[J].四川大学学报（自然科学版）,2017,54(1):76-80. 被引量：5
5蔡俊宁,黄文韬,韦敏志.一类(5,10)次Liénard方程的小振幅极限环（英文）[J].上海师范大学学报（自然科学版）,2018,47(3):383-388.
6赵立纯,赵晓月,刘敬娜,刘兵,赵慧燕,李媛.基于ALLEE效应麦蚜种群模型的几何分析[J].生物数学学报,2019,34(1):47-54.

1林发兴.STABILITY AND EXISTENCE OF PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS ON LIENARD SYSTEMS[J].Annals of Differential Equations,1997,13(3):248-253.
2Shao Xianxi.ON THE CENTER OF GENERALIZED LIENARD SYSTEM[J].Annals of Differential Equations,2006,22(4):551-559.
3刘朝杰,孙瑞德.THE UNIQUENESS OF THE SOLUTION OF LIENARD SYSTEM TO THE INITIAL VALUE PROBLEM[J].Annals of Differential Equations,2001,17(2):159-161. 被引量：2
4韩茂安,叶彦谦,朱德明.Cyclicity of homoclinic loops and degenerate cubic Hamiltonians[J].Science China Mathematics,1999,42(6):605-617. 被引量：2
5苏莉,李红海.一类具有全实Laplacian谱的有向图[J].浙江大学学报（理学版）,2011,38(6):614-619.
6Chen Shi\|hua, Feng Jian\|wen, Zeng Xian\|wu School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.The Cyclicity of the Period Annulus Around the Quadratic Isochronous Center[J].Wuhan University Journal of Natural Sciences,2001,6(4):754-758.
7HAN,Mao-an(韩茂安).ON SOME PROPERTIES OF LIENARD SYSTEMS[J].Applied Mathematics and Mechanics(English Edition),2002,23(4):454-462.
8黄立宏.ON THE CONTINUABILITY OF SOLUTIONS IN THE FUTURE FOR THE LIENARD SYSTEM[J].Annals of Differential Equations,1995,11(1):57-62.
9韩茂安.Cyclicity of planar homoclinic loops and quadratic integrable systems[J].Science China Mathematics,1997,40(12):1247-1258. 被引量：13
10Liqin Zhao,Weigu Li,Zhifen Zhang.Cyclicity of elementary polycycles and ensembles with codimension 3 degeneration[J].Chinese Science Bulletin,1998,43(22):1849-1864. 被引量：6

Annals of Differential Equations

1999年第2期

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LIAPUNOV CONSTANTS AND HOPF CYCLICITYOF LIENARD SYSTEMS 被引量：8

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引证文献8

二级引证文献6

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