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Limit cycles in a quartic system with a third-order nilpotent singular point
- Source :
- Advances in Difference Equations, Vol 2018, Iss 1, Pp 1-15 (2018)
- Publication Year :
- 2018
- Publisher :
- SpringerOpen, 2018.
-
Abstract
- Abstract In this paper, limit cycles bifurcating from a third-order nilpotent critical point in a class of quartic planar systems are studied. With the aid of computer algebra system MAPLE, the first 12 Lyapunov constants are deduced by the normal form method. As a result, sufficient and necessary center conditions are derived, and the fact that there exist 12 or 13 limit cycles bifurcating from the nilpotent critical point is proved by different perturbations. The result in [Qiu et al. in Adv. Differ. Equ. 2015(1):1, 2015] is improved.
Details
- Language :
- English
- ISSN :
- 16871847
- Volume :
- 2018
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.1fa2c3d2fe8f4511b6ca2ad3f70bef2b
- Document Type :
- article
- Full Text :
- https://doi.org/10.1186/s13662-018-1607-x