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非退化平面系统在平衡曲线附近的轨道结构

Orbit Structure near Equilibrium Curve of Non-degenerated Planar Systems
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摘要 讨论平面系统.x=A(x,y)y,.y=B(x,y)y在满足非退化条件A2(0,0)+B2(0,0)≠0时,在平衡流形y=0附近轨线的拓扑结构,并对平衡流形y=0上的点附近的一类向量场进行局部分类. In this paper,by studying the topological structure of the planar system =A(x,y)y,·↑y=B(x,y)y,the local classification of vector fields near the equilibrium manifold y=0 for the non-degenerated case A^2(0,0)+B^2(0,0)≠0 is obtained.
出处 《徐州师范大学学报(自然科学版)》 CAS 2008年第2期23-25,共3页 Journal of Xuzhou Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(10672062 10771113)
关键词 平衡曲线 轨道结构 equilibrium curve orbit structure
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参考文献7

  • 1Aulbach B. Continuous and discrete dynamics near manifolds of equilibra[M]//Lecture notes in math: 1058. New York: Springer-Verlag, 1984.
  • 2Fiedler B, Liebscher S, Alexander J C. Generic Hopf bifurcation from lines of equilibria without parameters I:Theory [J]. J Diff Equs,2000,167:16.
  • 3Fiedler B, Liebscher S. Generic Hopf bifurcation from lines of equilibria without parameters II: Systems of viscous hyperbolic balance laws[J]. SIAM J Math Anal,2000,31(6) :1396.
  • 4Fiedler B,Liebscher S, Alexander J C. Generic Hopf bifurcation from lines of equilibria without parameters Ⅲ:Binary osciUations[J]. Int J Bifur & Chaos,2000,10(7) : 1613.
  • 5Fiedler B,Liebscher S. Bifurcations without parameters: some ODE and PDE examples[C]//Proceedings of the International Congress of MathematiciansⅢ. Beijing: Higher Ed Press, 2002,3,305.
  • 6Hsu Sze-bi, Hwang Tzy-wei, Kuang Yang. Rich dynamics of a ratio-dependent one-prey two-predators model[J]. J Math Biol,2001,43:377.
  • 7张鑫,唐云,Rudolf Scherer.Stability Analysis of Equilibrium Manifolds for a Two-Predators One-Prey Model[J].Tsinghua Science and Technology,2006,11(6):739-744. 被引量:1

二级参考文献9

  • 1Sze-Bi Hsu,Tzy-Wei Hwang,Yang Kuang.Rich dynamics of a ratio-dependent one-prey two-predators model[J].Journal of Mathematical Biology.2001(5)
  • 2Sze-Bi Hsu,Tzy-Wei Hwang,Yang Kuang.Global analysis of the Michaelis–Menten-type ratio-dependent predator-prey system[J].Journal of Mathematical Biology.2001(6)
  • 3Robinson C.Dynamical Systems, Stability, Symbolic Dy- namics and Chaos ([]..1998
  • 4Lee J,,Chiang H-D.Theory of stability regions for a class of nonhyperbolic dynamical systems and its application to constraint satisfaction problems[].IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applica- tions.2002
  • 5Fiedler B,,Liebscher S.Generic Hopf bifurcation from lines of equilibria without parameters: Ⅱ, Systems of vis- cous hyperbolic balance laws[].SIAM Journal on Mathematical Analysis.2000
  • 6Hsu Sze-Bi,,Hwang Tzy-Wei,Kuang Yang.A ratio- dependent food chain model and its applications to bio- logical control[].Mathematical Biosciences.2003
  • 7Fiedler B,Liebscher S.Bifurcations without parameters: Some ODE and PDE examples[].ICM.2002
  • 8Fiedler B,,Liebscher S,Alexander J C.Generic Hopf bi- furcation from lines of equilibria without parameters: I, Theory[].Journal of Differential Equations.2000
  • 9Fiedler B,,Liebscher S,Alexander J C.Generic Hopf bi- furcation from lines of equilibria without parameters: Ⅲ, Binary oscillations[].International Journal of Bifurcation and Chaos.2000
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