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KUKLES SYSTEM WITH TWO FINE FOCI 被引量：1

KUKLES SYSTEM WITH TWO FINE FOCI
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摘要 A Kukles system with two fine foci is considered. We prove if the two finefoci have the same order, then the highest order of each fine focus is two; if thetwo fine fool have different order, and if the highest order of one of these two finefoci is one, then the highest order of the other is five. Based on these results wecan further prove that a Kukles system with two fine foci can generate at leastsix limit cycles. A Kukles system with two fine foci is considered. We prove if the two finefoci have the same order, then the highest order of each fine focus is two; if thetwo fine fool have different order, and if the highest order of one of these two finefoci is one, then the highest order of the other is five. Based on these results wecan further prove that a Kukles system with two fine foci can generate at leastsix limit cycles.
作者 吴勇宾 陈国维 杨信安
出处 《Annals of Differential Equations》 1999年第4期422-437,共16页 微分方程年刊（英文版）
关键词 fine focus limit cycles BIFURCATION fine focus, limit cycles, bifurcation
分类号 O175 [理学—基础数学]
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  • 1史松龄.二次系统(E2)出现至少四个极限环的例子[J].中国科学,1979(11):1051-1056.
  • 2LI J B. Hilbert' s 16th problem and bifurcations of planar polynomial vector fields[J]. International Journal of Bifurcation and Chaos, 2003, 13 (1): 47-106.
  • 3LI C Z, LIU C J, YANG J Z. A cubic system with thirteen limit cycles[J]. Journal of Differential Equations, 2009, 246(9) : 3609 -3619.
  • 4$HUBE A 5. On Kukles and Cherkas conditions for a cubic system[ J]. Differential Equations, 1993, 29 (4) : 625 -627.
  • 5CHAVARRIGA S J, GINE J. Integrability of a linear center perturbed by a fourth degree homogeneous polynomial [ J ]. Publicacions Matemhtiques, 1996, 40( 1 ) : 21 -39.
  • 6CHAVARRIGA S J, GINE J. lntegrability of a linear center perturbed by a fifth degree homogeneous polynomial[ J]. Publicacions Matemhtiques, 1997, 41(2) : 335 -356.
  • 7GINE J. Conditions for the existence of a center for the Kukles homogeneous systems [ J ]. Computers & Mathematics with Applications, 2002, 43 (10) : 1261 - 1269.
  • 8LLIBRE J, MEREU A C. Limit cycles for generalized Kukles polynomial differential systems [ J ]. Nonlinear Analysis: Theory, Methods & Appli- cations, 2011,74(4): 1261 -1271.
  • 9SAEZ E, SZANTO I. Bifurcations of limit cycles in Kukles systems of arbitrary degree with invariant ellipse [ J ]. Applied Mathematics Letters, 2012, 25(11) : 1695 -1700.
  • 10YU P, HAN M A. Twelve limit cycles in a cubic case of the 16th Hilbert problem[ J]. International Journal of Bifurcation and Chaos, 2005, 15 (7) : 2191 -2205.

引证文献1

Annals of Differential Equations
1999年 第4期

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