BIFURCATION OF LIMIT CYCLE AT THE INFINITY ON A CENTER MANIFOLDS IN SPACE VECTOR FIELD

Chaoxiong Du; Wentao Huang

doi:10.11948/20230254

2024 Volume 14 Issue 1

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Chaoxiong Du, Wentao Huang. BIFURCATION OF LIMIT CYCLE AT THE INFINITY ON A CENTER MANIFOLDS IN SPACE VECTOR FIELD[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 408-423. doi: 10.11948/20230254

Citation:

Chaoxiong Du, Wentao Huang. BIFURCATION OF LIMIT CYCLE AT THE INFINITY ON A CENTER MANIFOLDS IN SPACE VECTOR FIELD[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 408-423. doi: 10.11948/20230254

BIFURCATION OF LIMIT CYCLE AT THE INFINITY ON A CENTER MANIFOLDS IN SPACE VECTOR FIELD

Chaoxiong Du^1, ,,
Wentao Huang^2,

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

Author Bio: Email: huangwentao@163.com(W. Huang)
Corresponding author: Email: ducx123@126.com(C. Du)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12061016) and the Research Fund of Hunan provincial education department(No. 22A719)

Abstract

Abstract

In this paper, we deal with the problem of large amplitude limit cycles bifurcation at infinity in space vector field. By making two appropriate transformations and making use of singular values methods on a center manifold to compute focal values carefully, we obtain the simplified expressions of the first five focal values at the infinity by using symbolic calculation methods. Further, we show the infinity can bifurcate 5 large limit cycles.
- Space vector field /
- infinity /
- limit cycle bifurcation /
- focal values
MSC: 34C07, 34C23

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References

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