THE NUMBER OF LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP FOR A NEAR-HAMILTONIAN SYSTEM

Xiaoyu Xu; Junmin Yang; Tong Han

doi:10.11948/20230387

2024 Volume 14 Issue 2

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Xiaoyu Xu, Junmin Yang, Tong Han. THE NUMBER OF LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP FOR A NEAR-HAMILTONIAN SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1111-1132. doi: 10.11948/20230387

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Xiaoyu Xu, Junmin Yang, Tong Han. THE NUMBER OF LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP FOR A NEAR-HAMILTONIAN SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1111-1132. doi: 10.11948/20230387

THE NUMBER OF LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP FOR A NEAR-HAMILTONIAN SYSTEM

1.
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, China
2.
Golden Education, Hongkou District, Shanghai, 200083, China

Author Bio: Email: 13832174692@qq.com(X. Xu); Email: hantong@gaodun.com(T. Han)
Corresponding author: Email: jmyang@hebtu.edu.cn(J. Yang)
Fund Project: This project was supported by the National Natural Science Foundation of China (11971145)

Abstract

Abstract

In this paper, for a general near-Hamiltonian system we study the number and distributions of limit cycles near a double homoclinic loop. For a cubic Hamiltonian system with general polynomial perturbations, we obtain a lower bound of the maximum number of limit cycles near a double homoclinic loop.
- Limit cycle /
- Melnikov function /
- homoclinic loop /
- bifurcation
MSC: 34C07, 34C23

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References

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