INTEGRABILITY AND LIMIT CYCLES OF A SYMMETRIC 3-DIM QUADRATIC SYSTEM

Yongjun Li; Valery G. Romanovski

doi:10.11948/20200162

2021 Volume 11 Issue 5

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Yongjun Li, Valery G. Romanovski. INTEGRABILITY AND LIMIT CYCLES OF A SYMMETRIC 3-DIM QUADRATIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2230-2244. doi: 10.11948/20200162

Citation:

Yongjun Li, Valery G. Romanovski. INTEGRABILITY AND LIMIT CYCLES OF A SYMMETRIC 3-DIM QUADRATIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2230-2244. doi: 10.11948/20200162

INTEGRABILITY AND LIMIT CYCLES OF A SYMMETRIC 3-DIM QUADRATIC SYSTEM

Yongjun Li^1, ,,
Valery G. Romanovski^2,3,4, ,

1.
School of Mathematics, Lanzhou City University, Lanzhou, 730070, China
2.
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia
3.
Faculty of Natural Science and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
4.
Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia

Corresponding authors: li_liyong120@163.com(Y. Li); valerij.romanovskij@um.si(V. G. Ro manovski)
Fund Project: The first author is supported by the National Natural Science Foundation of China(11761044). The second author acknowledges the support of the work by the Slovenian Research Agency (program P1-0306, project N1-0063)

Abstract

Abstract

We study periodic solutions and first integrals in a three-dimensional quadratic system of ODEs. Coefficient conditions for existence of centers on center manifolds are obtained. Some bounds of the number of limit cycles bifurcating from the centers under small perturbations are given.
- Integrability /
- limit cycle /
- center /
- center manifold /
- polynomial system
MSC: 37G15, 37J15, 37J35

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References

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