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首页> 外文会议>IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics, Jan 4-8, 1999, Madras, Chennai, India >STOCHASTIC STABILITY AND BIFURCATION OF QUASI-HAMILTONIAN SYSTEMS
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STOCHASTIC STABILITY AND BIFURCATION OF QUASI-HAMILTONIAN SYSTEMS

机译：拟哈密顿系统的随机稳定性和分支

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摘要

The paper consists of two parts. In the first part the stochastic averaging of quasi-integrable-Hamiltonian systems with real noise excitations is introduced. The expression for the largest Lyapunov exponent of the square root of the Hamiltonian is formulated by generalizing the Khasminskii's procedure to the averaged systems, based on which the stochastic stability and bifurcation of the original systems are studied. In the second part, an n-degree-of-freedom quasi-non-integrable-Hamiltonian system is reduced to an Ito equation of one-dimensional averaged Hamiltonian by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. The necessary and sufficient conditions for the asymptotic stability in probability of the trivial solution and the condition for the Hopf bifurcation of the original systems are obtained approximately by examining the sample behaviors of the one-dimensional diffusion process of the square-root of averaged Hamiltonian and the averaged Hamiltonian, respectively, at the two boundaries.
机译：本文由两部分组成。在第一部分中，介绍了具有实际噪声激励的拟可积分哈密顿系统的随机平均。哈密​​顿量平方根的最大Lyapunov指数的表达式是通过将Khasminskii程序推广到平均系统而得出的，在此基础上，研究了原始系统的随机稳定性和分叉性。在第二部分中，通过使用拟非积分Hamiltonian系统的随机平均方法，将n自由度拟不可积分Hamiltonian系统简化为一维平均哈密顿方程的Ito方程。通过检查平均哈密顿量和平方根的一维扩散过程的样本行为，近似地获得了平凡解的概率渐近稳定性和原始系统的Hopf分支条件的充要条件。在两个边界处的平均哈密顿量。

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