| 具有两条实或虚直线解的系统 X|.=-ax-by+sum from i+j=3 a_(ij)x~iy~j,y|.=cx+dy |
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| 引用本文： | 沈伯骞,索光俭.具有两条实或虚直线解的系统 X|.=-ax-by+sum from i+j=3 a_(ij)x~iy~j,y|.=cx+dy[J].辽宁师范大学学报(自然科学版),1987(1). |
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| 作者姓名： | 沈伯骞 索光俭 |
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| 作者单位： | 数学系，吉林师范学院 |
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| 摘 要： | 本文给出了当实系统X|.=-ax-by+sum from i+j=3 a_(ij)x~iy~j,y|.=cx+dy具有两条相交实直线解或两条共轭虚直线解时的一般形式。我们证明了,若此系统具有两条相交实直线解,则此系统不存在极限环;若此系统具有两条共轭虚直线解,则此系统至多存在一个极限环。关于极限环唯一性的证明,我们应用了Dulac函数。本文还给出了此系统恰好存在一个极限环的充分必要条件。
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| 关 键 词： | 实直线解 虚直线解 三次系统 |
The Real System X|.=-ax-by+sum from i+j=3 a_(ij)x~iy~j,y|.=cx+dy. With Two Real or Imaginary Straight Line Solution |
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| Shen Poqian.The Real System X|.=-ax-by+sum from i+j=3 a_(ij)x~iy~j,y|.=cx+dy. With Two Real or Imaginary Straight Line Solution[J].Journal of Liaoning Normal University(Natural Science Edition),1987(1). |
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| Authors: | Shen Poqian |
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| Institution: | Shen Poqian(Department of Mathematical) Suo Guangjian(Jilin Normal Institute) |
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| Abstract: | This paper gives out general form of real system which possesses two intersective real straight line solutions or two conjugate imaginary straight line solutions. in which we proved that if this system possesses two intersective real straight line solutions, then it has no any limit cycles. if this system possesses two conjugate imaginary straight line solution, then it possesses at most one limit cycle, in regard to prove the uniqueness of limit cycle. we applied Dulac function method, moreover, this paper gives out the necessary and sufficient condition of this system that it possesses just one limit cycle. |
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| Keywords: | Real straight line Solutions imaginary straight line solutions Cubic systems |
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