HOPF BIFURCATION AT A DEGENERATE SINGULAR POINT IN 3-DIMENSIONAL VECTOR FIELD

Chaoxiong Du; Wentao Huang

doi:10.11948/20210090

2021 Volume 11 Issue 6

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Chaoxiong Du, Wentao Huang. HOPF BIFURCATION AT A DEGENERATE SINGULAR POINT IN 3-DIMENSIONAL VECTOR FIELD[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3001-3013. doi: 10.11948/20210090

Citation:

Chaoxiong Du, Wentao Huang. HOPF BIFURCATION AT A DEGENERATE SINGULAR POINT IN 3-DIMENSIONAL VECTOR FIELD[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3001-3013. doi: 10.11948/20210090

HOPF BIFURCATION AT A DEGENERATE SINGULAR POINT IN 3-DIMENSIONAL VECTOR FIELD

Chaoxiong Du^1, ,,
Wentao Huang²

1.
School of Mathematics, Changsha Normal University, Changsha, Hunan, 410100, China
2.
College of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, Guangxi, China

Corresponding author: Email: ducx123@126.com(C. Du)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061016) and the Research Fund of Hunan provincial education department(18A525) and the Hunan provincial Natural Science Foundation of China (2020JJ4630)

Abstract

Abstract

The work of this paper focuses on investigating limit cycle bifurcation for a degenerate singular point in 3-Dimensional vector fields. By making two appropriate transformations and making use of singular values methods to compute focal values carefully, we give the expressions of the first five Lyapunov constants at the origin that is a degenerate singular point. Moreover, we obtain the considered system can bifurcate 5 limit cycles near the origin. In terms of results on limit cycle bifurcation from degenerate singular point in 3-Dimensional vector field, it is less seen in published references..
- 3-Dimensional vector field /
- degenerate singular point /
- limit cycle bifurcation /
- focal values
MSC: 34C07, 34C23

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References

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