On the kolmogorov system with fourth-degree homogeneous nonlinearities
https://doi.org/10.29235/1561-8323-2020-64-3-268-272
Abstract
The necessary conditions of the center at the singular point O (0, 0) for the kolmogorov system with fourth-degree homogeneous nonlinearities are found in the work of B. Ferenc, J. Dzheny, W. Liu, V. G. Romanovsky. For all these cases, with the exception of two, sufficiency is also proved. In the present article, sufficiency is proved for two cases of the center that were not proved in the above-mentioned work. In addition, the sufficiency of two other conditions of the center is proved in another way.
About the Author
A. P. Sadovskii
Belarusian State University
Belarus
Belarus
Sadovskii Anton Pavlovich – D. Sc. (Physics and Mathematics), Professor
4, Nezavisimosti Ave, 220030, Minsk
References
1. Ferčec B., Gine J., Liu y., Romanovski V. G. Integrability Conditions for Lotka–Volterra Planar Complex Quartic Systems Hoving Homogeneous Nonlinearities. Acta Applicandae Mathematicae, 2013, vol. 124, no. 1, pp. 107–122. https://doi.org/10.1007/s10440-012-9772-5
2. Sadovskii A. P. Center conditions for a system with homogeneous nonlinearities. Trudy Mezhdunarodnoi konferentsii po differentsial’nym uravneniyam «Eruginskie chteniya–2007» [Proceedings of the International Conference on Differential Equations “Eruginskie Chteniya–2007”]. Minsk, 2007, pp. 156–167 (in Russian).
3. Sadovskii A. P. On one case of the center of a system with homogeneous non-linearities of the fourth degree. Materialy konferentsii «Eruginskie chteniya–2018». Minsk, 15–18 maya 2018. Chast’ 1 [Proceedings of the conference “Eruginskie Chtenija–2018”. Minsk, May 15–18, 2018. Part 1]. Minsk, 2018, pp. 91–93 (in Russian).
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