On integrability and cyclicity of cubic systems
In this paper we study the integrability of a few families of the complex cubic system. We have obtained necessary and sufficient conditions for existence of a local analytic first integral. Sufficiency of the obtained conditions was proven using different methods: time-reversibility, Darboux integr...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2020.1.55 |
| Online Access: | http://acta.bibl.u-szeged.hu/70939 |
| Tartalmi kivonat: | In this paper we study the integrability of a few families of the complex cubic system. We have obtained necessary and sufficient conditions for existence of a local analytic first integral. Sufficiency of the obtained conditions was proven using different methods: time-reversibility, Darboux integrability and others. Using the obtained results on integrability of complex cubic system, we have obtained results for corresponding real cubic systems. Then the study of bifurcation of limit cycles from each component of the center variety of real system was performed. |
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| ISSN: | 1417-3875 |