BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS

Yinlai Jin; Dongmei Zhang; Ningning Wang; Deming Zhu

doi:10.11948/20230052

2023 Volume 13 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2906-2921

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Yinlai Jin, Dongmei Zhang, Ningning Wang, Deming Zhu. BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2906-2921. doi: 10.11948/20230052

Citation:

Yinlai Jin, Dongmei Zhang, Ningning Wang, Deming Zhu. BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2906-2921. doi: 10.11948/20230052

BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS

1.
School of Mathematics and Statistics, Linyi University, 276005 Linyi, Shandong, China
2.
School of Mathematics and Statistics, Shandong Normal University, 250014 Jinan, China
3.
School of Mathematical Sciences, East China Normal University, 200062 Shanghai, China

Author Bio: Email: wangningningx1y2z34@126.com(N. Wang); Email: dmzhu@math.ecnu.edu.cn(D. Zhu)
Corresponding authors: Email: jinyinlai@lyu.edu.cn(Y. Jin); Email: zhangdongmei@lyu.edu.cn(D. Zhang)
Fund Project: The authors were supported by Natural Science Foundation of Shandong Province (ZR2018MA016, ZR2015AL005), National Natural Science Foundation of China (11902133, 12071198, 11601212) and the Applied Mathematics Enhancement Program of Linyi University

Abstract

Abstract

In the paper, under twisted conditions, we consider the bifurcation problem of the fine heteroclinic loop with two hyperbolic critical points for high-dimensional systems. By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits as the local coordinate system in the small tubular neighborhood of the heteroclinic loop, we construct the Poincaré maps and obtain the bifurcation equations. Then, by considering the small nonnegative solutions of the bifurcation equations, we get the main results of the reservation of the heteroclinic orbits, the existence and existence regions, the coexistence and coexistence regions of the 1-homoclinic loop, 1-periodic orbit, 2-homoclinic loop and 2-periodic orbit. Moreover, the bifurcation surfaces and graphs are given.
- Twist /
- fine /
- heteroclinic loop /
- bifurcation /
- high-dimensional system
MSC: 34C23, 34C37, 37C29

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References

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