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首页> 外文期刊>International journal of non-linear mechanics >Stochastic stability of quasi-integrable and resonant Hamiltonian systems under parametric excitations of combined Gaussian and Poisson white noises
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Stochastic stability of quasi-integrable and resonant Hamiltonian systems under parametric excitations of combined Gaussian and Poisson white noises

机译：高斯和泊松混合白噪声参数激励下拟可积和共振哈密顿系统的随机稳定性

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摘要

A procedure for determining the asymptotic Lyapunov stability with probability one of multi-degree-of-freedom (MDOF) quasi-integrable and resonant Hamiltonian systems under parametric excitations of combined Gaussian and Poisson white noises is proposed. For the case of resonance with α resonant relations, the averaged lto stochastic differential equations (SDEs) for quasi-integrable and resonant Hamiltonian systems subject to parametric excitations of combined Gaussian and Poisson white noises are first derived by using the stochastic averaging method. Then, the expression for the largest Lyapunov exponent is obtained by generalizing Khasminskii's procedure to the averaged Ito SDEs and using the property of the stochastic integro-differential equations (SIDEs). Finally, the stochastic stability of the original system is determined approximately by using the largest Lyapunov exponent. An example of two non-linear damping oscillators under parametric excitations of combined Gaussian and Poisson white noises is worked out to illustrate the application of the proposed procedure. The validity of the proposed procedure is verified by the good agreement between the analytical results and those from Monte Carlo simulation.
机译：提出了一种在高斯和泊松混合白噪声的参数激励下，以多自由度（MDOF）准可积和共振哈密顿系统为概率确定渐近李雅普诺夫稳定性的方法。对于具有α共振关系的共振，首先采用随机平均法推导受积分高斯和泊松白噪声参数激励的准可积分和共振哈密顿系统的平均lto随机微分方程（SDE）。然后，通过将Khasminskii程序推广到平均Ito SDE并利用随机积分微分方程（SIDEs）的性质，获得最大Lyapunov指数的表达式。最后，通过使用最大的Lyapunov指数近似确定原始系统的随机稳定性。研究了在组合高斯和泊松白噪声的参数激励下两个非线性阻尼振荡器的例子，以说明所提出程序的应用。分析结果与蒙特卡洛模拟结果之间的良好一致性验证了所提方法的有效性。

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