FLIP BIFURCATION WITH RANDOM EXCITATION

Diandian Tang; Jingli Ren

doi:10.11948/20220042

2022 Volume 12 Issue 6

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Diandian Tang, Jingli Ren. FLIP BIFURCATION WITH RANDOM EXCITATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2488-2510. doi: 10.11948/20220042

Citation:

Diandian Tang, Jingli Ren. FLIP BIFURCATION WITH RANDOM EXCITATION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2488-2510. doi: 10.11948/20220042

FLIP BIFURCATION WITH RANDOM EXCITATION

Diandian Tang¹,
Jingli Ren^1, ,

1.
School of Mathematics and Statistics/Henan Academy of Big Data, Zhengzhou University, Zhengzhou, 450001, China

Corresponding author: Email address: renjl@zzu.edu.cn(J. Ren)
Fund Project: The authors were supported by the National Natural Science Foundation of China (52071298) and ZhongYuan Science and Technology Innovation Leadership Program (214200510010)

Abstract

Abstract

In this paper, flip bifurcation with random excitation is studied by employing the methods of normal forms, Picard iterations and orthogonal polynomial approximation. For the codimension one case, a Neimark-Sacker bifurcation, a 1:2 resonance and a fold-flip bifurcation are detected. It is found that the system undergoes heteroclinic bifurcation and homoclinic bifurcation near 1:2 resonance point, a hopf bifurcation and a cusp bifurcation near fold-flip bifurcation point. For the codimension two case, the system undergoes only a flip bifurcation when random excitation is imposed on the nonlinear term. In addition, numerical simulations are given to show the disparity between the codimension one and two cases.
- Flip bifurcation /
- random excitation /
- Neimark-Sacker bifurcation /
- 1:2 resonance /
- fold-flip bifurcation
MSC: 34C23, 37G10

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References

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