Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point
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In this paper, integrability problem and bifurcation of limit cycles for cubic Kukles systems which are assumed to have a nilpotent origin are investigated. A complete classification is given on the integrability conditions and proven to have a total of 7 cases. Bifurcation of limit cycles is also discussed; six or seven limit cycles can be obtained by two different perturbation methods. Integrability problem and bifurcation of limit cycles for the cubic Kukles systems with a nilpotent origin have been completely solved.
KeywordsKukles system Center–focus problem Nilpotent singular point Normal form Integrability
We thank the anonymous reviewer for his/her valuable and detailed comments which have greatly improved our paper. This research was partially supported by the National Natural Science Foundation of China (Nos. 11601212, 2017A030313010,11501055), Natural Science Foundation of Shandong Province (No. ZR2018MA002) and Science and Technology Program of Guangzhou (No. 201707010426).
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Conflict of interest
The authors declare that they have no conflict of interest.
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