THE NUMBER OF LIMIT CYCLES FROM A QUARTIC CENTER BY THE HIGHER-ORDER MELNIKOV FUNCTIONS

Liu Xia

doi:10.11948/20200208

2021 Volume 11 Issue 3

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Liu Xia. THE NUMBER OF LIMIT CYCLES FROM A QUARTIC CENTER BY THE HIGHER-ORDER MELNIKOV FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1405-1421. doi: 10.11948/20200208

Citation:

Liu Xia. THE NUMBER OF LIMIT CYCLES FROM A QUARTIC CENTER BY THE HIGHER-ORDER MELNIKOV FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1405-1421. doi: 10.11948/20200208

THE NUMBER OF LIMIT CYCLES FROM A QUARTIC CENTER BY THE HIGHER-ORDER MELNIKOV FUNCTIONS

Liu Xia^1,2, ,

1.
College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China
2.
College of Mathematics and Information Science, Henan Normal University, 453007, China

Corresponding author: Email address: liuxiapost@163.com(X. Liu)
Fund Project: The author was supported by National Natural Science Foundation of China (11601131)

Abstract

Abstract

In this paper, by computing the higher-order Melnikov functions we study the number of limit cycles of the system $ \dot{x} = -y(1+x)^3+\epsilon P(x, y), $ $ \dot{y} = x(1+x)^3-\epsilon Q(x, y) $ where $ P(x, y) $ and $ Q(x, y) $ are arbitrary cubic polynomials. Our main results show that the first four Melnikov functions associated with the perturbed system yield at most five limit cycles.
- Melnikov functions /
- bifurcation /
- limit cycles /
- generators
MSC: 34C05, 34C07, 37G15

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References

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