Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems
Lyapunov Exponents and Stochastic Stability of Quasi-Integrable-Hamiltonian Systems
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DOI：
10.1115/1.2789148
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发表时间：
1999-03
期刊：
影响因子：
--
通讯作者：
W. Zhu;Z. L. Huang
中科院分区：
文献类型：
--
作者：
W. Zhu;Z. L. Huang
本文首次导出了多自由度可积非共振哈密顿系统在小强度真实噪声激励和光阻尼下的平均方程。然后，将Khasminskii的最大Lyapunov指数推广到平均方程，得到了哈密顿量平方根的最大Lyapunov指数的表达式，由此可以近似地确定原系统的随机稳定性和分叉现象。以两自由度线性和非线性随机系统为例，说明了拟可积哈密顿系统的随机平均法和Khasminskii过程相结合的方法的应用。
The averaged equations of integrable and non resonant Hamiltonian systems of multi-degree-of-freedom subject to light damping and real noise excitations of small intensities are first derived. Then, the expression for the largest Lyapunov exponent of the square root of the Hamiltonian is formulated by generalizing the well-known procedure due to Khasminskii to the averaged equations, from which the stochastic stability and bifurcation phenomena of the original systems can be determined approximately. Linear and nonlinear stochastic systems of two degrees-of-freedom are investigated to illustrate the application of the proposed combination approach of the stochastic averaging method for quasi-integrable Hamiltonian systems and Khasminskii's procedure.