Gauss白噪声激励下时滞悬架系统的随机分岔

兰盼; 魏周超

doi:10.21656/1000-0887.450343

Gauss白噪声激励下时滞悬架系统的随机分岔

doi: 10.21656/1000-0887.450343

兰盼^{1, 2,},
魏周超^{1, 2, ,}

1.
西南交通大学轨道交通运载系统全国重点实验室, 成都 610031
2.
中国地质大学(武汉) 数学与物理学院，武汉 430074

基金项目:

国家自然科学基金 12172340

国家自然科学基金 12411530068

轨道交通运载系统全国重点实验室开放课题 RVL2501

详细信息

作者简介:
兰盼(2000—)，女，硕士生(E-mail: lanpan1128@163.com)

通讯作者:
魏周超(1984—)，男，教授，博士，博士生导师(通讯作者. E-mail: weizhouchao@163.com)

中图分类号: O32
计量
- 文章访问数: 104
- HTML全文浏览量: 27
- PDF下载量: 29
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-30
- 修回日期: 2025-04-22
- 刊出日期: 2025-12-01

Random Bifurcation of Time-Delay Suspension Systems Under Gaussian White Noise Excitation

LAN Pan^{1, 2
,},
WEI Zhouchao^{1, 2
, ,}

1.
State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu 610031, P.R. China
2.
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074, P.R. China

摘要

摘要: 研究了具有随机激励和时滞反馈控制的悬架系统. 首先，分析系统发生Hopf分岔的条件. 其次，利用中心流形理论和最大Lyapunov指数，研究系统的局部稳定性和随机D分岔条件，并通过奇异边界理论探讨了系统的全局稳定性. 最后，通过数值模拟揭示了噪声强度和时滞反馈系数对系统动力学的影响，并验证了理论结果.
- 悬架系统 /
- Gauss噪声激励 /
- 时滞反馈控制 /
- 随机分岔 /
- 随机平均法
Abstract: The suspension system under random excitation and time-delay feedback control was investigated. Firstly, the conditions for the Hopf bifurcation of the system were analyzed. Secondly, the center manifold theory and the maximum Lyapunov exponent were used to study the local stability and stochastic D-bifurcation conditions for the system. Then the global stability was further explored with the singular boundary theory. Numerical simulations reveal the effects of noise intensities and time-delay feedback coefficients on the system dynamics, thereby verifying the theoretical results.
- suspension system /
- Gauss noise excitation /
- time-delay feedback control /
- stochastic bifurcation /
- stochastic average method

HTML全文

图 1 噪声强度δ=0.376，u₁/u₃=1.96＜2的分岔行为

Figure 1. The bifurcation behavior for noise intensity δ=0.376, u₁/u₃=1.96 < 2

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图 2 噪声强度δ=0.386，u₁/u₃=2.00的分岔行为

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. The bifurcation behavior for noise intensity δ=0.386, u₁/u₃=2.00

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图 3 噪声强度δ=0.48，u₁/u₃=2.31>2的分岔行为

Figure 3. The bifurcation behavior for noise intensity δ=0.48, u₁/u₃=2.31>2

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图 4 噪声强度δ=0.386，g₂=0.104 5，u₁/u₃=1.87＜2的分岔行为

Figure 4. The bifurcation behavior for noise intensity δ=0.386, g₂=0.104 5, u₁/u₃=1.87 < 2

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图 5 噪声强度δ=0.386，g₂=0.104 539，u₁/u₃=2.00的分岔行为

Figure 5. The bifurcation behavior for noise intensity δ=0.386, g₂=0.104 539, u₁/u₃=2.00

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图 6 噪声强度δ=0.386，g₂=0.104 6，u₁/u₃=2.21>2的分岔行为

Figure 6. The bifurcation behavior for noise intensity δ=0.386, g₂=0.104 6, u₁/u₃=2.21>2

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