THE BIFURCATION PROBLEMS OF HETEROCLINIC LOOPS FOR A CLASS OF HIGH-DIMENSIONAL SYSTEMS

Siqi Cao; Yinlai Jin; Deming Zhu

doi:10.11948/20260088

2027 Volume 17 Issue 2

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Siqi Cao, Yinlai Jin, Deming Zhu. THE BIFURCATION PROBLEMS OF HETEROCLINIC LOOPS FOR A CLASS OF HIGH-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1183-1201. doi: 10.11948/20260088

Citation:

Siqi Cao, Yinlai Jin, Deming Zhu. THE BIFURCATION PROBLEMS OF HETEROCLINIC LOOPS FOR A CLASS OF HIGH-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1183-1201. doi: 10.11948/20260088

THE BIFURCATION PROBLEMS OF HETEROCLINIC LOOPS FOR A CLASS OF HIGH-DIMENSIONAL SYSTEMS

1.
School of Mathematics and Statistics, Linyi University, 276005 Linyi, Shandong, China
2.
School of Mathematical Sciences, East China Normal University, 200062 Shanghai, China

Author Bio: Email: dmzhu@math.ecnu.edu.cn(D. Zhu)
Corresponding authors: Email: caosiqi1225@163.com(S. Cao); Email: jinyinlai@lyu.edu.cn(Y. Jin)
Fund Project: The authors were supported by Natural Science Foundation of Shandong Province (ZR2018MA016), National Natural Science Foundation of China (12471166)

Abstract

Abstract

In this paper, we study the bifurcation problems of heteroclinic loops with two hyperbolic critical points for high-dimensional systems under the condition that the product of hyperbolic ratios is greater than 1. Using exponential dichotomy, the local coordinate systems and Poincaré maps are constructed in the small tubular neighborhood of heteroclinic loop. Under twisted and non-twisted conditions, we obtain existence and number of 1-homoclinic loop, 1-periodic orbit, two 1-periodic orbits and double 1-periodic orbit. In addition, the corresponding bifurcation surfaces and bifurcation diagrams are also given.
- Heteroclinic loop /
- high-dimensional system /
- bifurcation /
- Poincarémap /
- periodic orbit
MSC: 34C23, 34C37, 37C29

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References

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