| 平面多体机械系统的随机稳定性及Hopf分岔分析 |
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| 作者单位： | ;1.兰州交通大学数理学院;2.兰州交通大学交通运输学院 |
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| 摘 要： | 首先建立平面多体机械系统的随机非线性动力学模型,得到It随机微分方程,求解了系统响应扩散过程的转移概率密度函数相应的FPK方程.然后运用拟不可积Hamilton理论对平面多体机械系统进行Hopf分岔分析,利用Lyapunov指数和奇异边界理论对该系统的局部和全局稳定性分别进行讨论.最后通过模拟平稳概率密度函数和联合概率密度函数的图像验证了理论结果.
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| 关 键 词： | 平面多体机械系统 拟不可积Hamilton理论 随机平均法 随机稳定性 随机Hopf分岔 |
Stochastic Stability and Hopf Bifurcation Behavior of Planar Multi-Body Mechanical System |
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| Institution: | ,School of Mathematics and Physics,Lanzhou Jiaotong University,School of Traffic and Transportation,Lanzhou Jiaotong University |
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| Abstract: | Firstly,the stochastic nonlinear dynamic model of the multi-body mechanical system was established,the It differentiation equation and the corresponding FPK equation of the response-transition probability density function with the diffusing process were obtained. Then,the Hopf bifurcation behavior of the planar multi-body mechanical system was studied by using the quasi-nonintegrable Hamilton system theory.The conditions of local and global stability of the system were discussed by largest Lyapunov exponent and boundary category.Finally,the functional image of stationary probability density and jointly stationary probability density were simulated to verify the theorectical results. |
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| Keywords: | multi-body mechanical system quasi-nonintegrable Hamilton system theory stochastic stability stochastic Hopf bifurcation |
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