A cubic system with thirteen limit cycles☆

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Abstract

We construct a planar cubic system and demonstrate that it has at least 13 limit cycles. The construction is essentially based on counting the number of zeros of some Abelian integrals.

Keywords

Cubic system
Limit cycles
Abelian integral
Hilbert's 16th problem

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This work is partially supported by grants NSFC 10671005 and NSFC 10831003 (C. Li), China Postdoctoral Science Foundation and NSFC 10871006 (C. Liu), and by grants NSFC 10571002, NSFC 10871006 and NSF of Beijing 1072002 (J. Yang).

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