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关于同宿分支的Leontovich分界线量

骆海英 李继彬

骆海英, 李继彬. 关于同宿分支的Leontovich分界线量[J]. 应用数学和力学, 2005, 26(4): 418-425.
引用本文: 骆海英, 李继彬. 关于同宿分支的Leontovich分界线量[J]. 应用数学和力学, 2005, 26(4): 418-425.
LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.
Citation: LUO Hai-ying, LI Ji-bin. What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation[J]. Applied Mathematics and Mechanics, 2005, 26(4): 418-425.

关于同宿分支的Leontovich分界线量

基金项目: 国家自然科学基金(重大)资助项目(40221503;40233029)
详细信息
    作者简介:

    骆海英(1978- ),女,河南人,博士(联系人.Tel:+86-10-62043430;Fax:+86-10-62043526;E-mail:hyluo@mail.iap.ac.cn).

  • 中图分类号: O175.14

What Are the Separatrix Values Named by Leontovich on Homoclinic Bifurcation

  • 摘要: 由Leontovich定义的鞍点量和分界线量是判断同宿轨道分支出极限环的数目及同宿环稳定性的主要判据.利用Tkachev对多重极限环稳定性判定的方法,对给定的系统,得到了同宿环分支的第三阶分界线量的公式,并对高阶分界线量做了猜测.
  • [1] Andronov A A,Leontovich E A,Gordon I I,et al.Theory of Bifurcations of Dynamical Systems on a Plane[M].New York:John Wiley & Sons, 1973.
    [2] 冯贝叶,钱敏.鞍点分界线环的稳定性及其分支出极限环的条件[J].数学学报,1985,28(1):53—70.
    [3] Joyal P.Generalized Hopf bifurcation and its dual, generalized homoclinic bifurcation[J].SIAM J Appl Math,1988,48(3):481—496. doi: 10.1137/0148027
    [4] Leontovich E A.On the generation of limit cycles from a separatrix[J].Dokl Acad Nauka,1951,78(4):641—644.
    [5] Roussarie R.On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields[J].Bol Soc Brasil Mat,1986,17(1):67—101. doi: 10.1007/BF02584827
    [6] Roussarie R.A note on finite cyclicity and Hilbert's 16th problem[A].In:Bamom R,Labarca J,Palis Jr,et al Eds.Dynamical Systems, Valparaiso 1986,Lecture Notes in Math[C].1331.New York: Springer-Verlag,1988,161—168.
    [7] Roussarie R.Techniques in the theory of local bifurcations: cyclicity and desingularization[A].In:Schlomiuk D Ed.Bifurcations and Periodic Orbits of Vector Fields[C].NATO ASI Series C.408.London:Kluwer Academic Publishers,1993,347—382.
    [8] LIU Yi-rong,LI Ji-bin.Theory of values of singular point in complex autonomous differential systems[J].Science in China,1990,33(1):10—23.
    [9] CAI Sui-lin,ZHANG Ping-guang.A quadratic system with a weak saddle II[J].Ann Differantial Equations,1988,4(2):131—142.
    [10] Amelikin B B,Lukashivich H A,Sadovski A P.Nonlinear Oscillations in Second Order Systems[M].Minsk: BGY lenin B I Press,1982.
    [11] 李伟固.正规型理论及其应用[M].北京: 北京科技出版社,2000.
    [12] Hilbert D.Mathematical problems[J].Proceeding of Symposia in Pure Mathematics,1976,28(1):1—34.
    [13] LUO Ding-jun,WANG Xian,ZHU De-ming,et al.Bifurcation Theory and Methods of Dynamical Systems[M].Singapore:World Scientific,1997.
    [14] Perko L M.Differential Equations and Dynamical Systems[M].New York: Springer-Verlag, 1991.
    [15] 叶彦谦.极限环论[M].上海:上海科技出版社,1984.
    [16] 张芷芬,丁同仁,黄文灶,等.微分方程定性理论[M].上海:上海科技出版社,1995.
    [17] 胡锐,冯贝叶.确定多重极限环的半稳定性及对二阶临界同宿环稳定性的判定[A].见:国际动力系统和常微分方程会议,北京,2001.
    [18] Ткачев В Ф.Необходимые и достаточные условия устойчивости полуустойчивости и неустойчивости предельного цикла и некоторые их приложения[J].Математический Сворник,1962,56(3):281—300.
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出版历程
  • 收稿日期:  2003-06-20
  • 修回日期:  2004-12-03
  • 刊出日期:  2005-04-15

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