Limit cycle containing nine critical points in its interior for a class of cubic systems

Yi-rong Liu; Ping Xiao

doi:10.1007/s11771-000-0045-5

Journal of Central South University ›› 2000, Vol. 7 ›› Issue (2) : 111 -112. DOI: 10.1007/s11771-000-0045-5

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Limit cycle containing nine critical points in its interior for a class of cubic systems

Yi-rong Liu ¹
, Ping Xiao ¹

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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.

Keywords

cubic systems / critical point of nine orders / limit cycle

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Yi-rong Liu, Ping Xiao. Limit cycle containing nine critical points in its interior for a class of cubic systems. Journal of Central South University, 2000, 7(2): 111-112 DOI:10.1007/s11771-000-0045-5

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References

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