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Applied Mathematics and Mechanics (English Edition) ›› 1994, Vol. 15 ›› Issue (5): 471-483.

• 论文 • 上一篇    下一篇

ON THE (1, 3) DISTRIBUTIONS OF LIMIT CYCLES OF PLANE QUADRATIC SYSTEMS

蔺小林1, 党新益2   

  1. 1. Northwest Institute of Light Industry Xianyang;
    2. Department of Mathematics Northwest University, Xian
  • 收稿日期:1992-02-28 出版日期:1994-05-18 发布日期:1994-05-18

ON THE (1, 3) DISTRIBUTIONS OF LIMIT CYCLES OF PLANE QUADRATIC SYSTEMS

Lin Xiao-lin1, Dang xin-yi2   

  1. 1. Northwest Institute of Light Industry Xianyang;
    2. Department of Mathematics Northwest University, Xian
  • Received:1992-02-28 Online:1994-05-18 Published:1994-05-18

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摘要： In this paper, (a) we rerise Theorem 2 of Ref [1] omit the condition V7>0.(b) we discuss the relative positions of six curves M(s2, r)=0, J(s2, r)=0, L(s2,r)=0, T(s2,r)=0,s2=s+2 and s2=s-2 Under the condition of the (1.3) distri-butions of limit cycles, we expand the variable regions of parameters (s, r) and clearly. show them in figure, (c) we study the (1, 3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite: and (d) we give a generalmethod to discuss the (1, 3) distibutions`of limit cycles of system (1.1) whatever there isone, two or three singular points at the infinite.

关键词: eigenfunction expansion variational method, periodic crack, stress intensity factor, T-stress, quadratic system, limit cycle

Abstract: In this paper, (a) we rerise Theorem 2 of Ref [1] omit the condition V7>0.(b) we discuss the relative positions of six curves M(s2, r)=0, J(s2, r)=0, L(s2,r)=0, T(s2,r)=0,s2=s+2 and s2=s-2 Under the condition of the (1.3) distri-butions of limit cycles, we expand the variable regions of parameters (s, r) and clearly. show them in figure, (c) we study the (1, 3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite: and (d) we give a generalmethod to discuss the (1, 3) distibutions`of limit cycles of system (1.1) whatever there isone, two or three singular points at the infinite.

Key words: eigenfunction expansion variational method, periodic crack, stress intensity factor, T-stress, quadratic system, limit cycle

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