Abstract
Discuss a class of real planar cubic systems with a critical point O(0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O(0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior.
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References
YE Yan-qian. Qualitative theory of polynomial differential systems (in Chinese) [M]. Shanghai: Shanghai Scientific and Technical Publishers, 1995
ZHANG Zi-feng, Ding Tong-ren, Huang Wen-zao, et al. Qualitative theory of differential equations [M]. American Mathematical Society, 1992
LIU Yi-rong. Multiplicity of higher order singular point of differential autonomous system [J]. J Central South Univ Tech (in Chinese), 1999, 30(3): 325–326
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Foundation item: The Natural Science Foundation of Hunan Province (No.97JJN-70)
Biography of the first author: LIU Yi-rong, professor, born in 1953, majoring in qualitative theory of differential equations.
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Liu, Yr., Xiao, P. Limit cycle containing nine critical points in its interior for a class of cubic systems. J Cent. South Univ. Technol. 7, 111–112 (2000). https://doi.org/10.1007/s11771-000-0045-5
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DOI: https://doi.org/10.1007/s11771-000-0045-5