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中文摘要：
推导非高斯白噪声激励下多自由度非线性系统所满足的广义It?随机微分方程、广义FPK方程、广义后向Kolmogorov方程及广义Pontryagin方程；提出在弱非高斯随机激励下多自由度非线性系统的随机平均法，导出随机平均的广义It?方程、广义FPK方程、广义后向Kolmogorov方程及广义Pontryagin方程。发展求解上述各方程的方法，通过求解这些方程得到非高斯随机激励的非线性系统的响应与可靠性；建立最大Lyapunov指数的计算公式，以此判别非高斯随机激励的多自由度非线性系统的概率为1稳定性与随机分岔；用上述方法研究典型多自由度非线性系统，并以数字模拟结果验证上述方法的正确性与精度。通过三年研究，初步建立起一套非高斯随机激励下多自由度非线性系统的随机动力学理论方法，并力求将它们应用于工程、物理、生物、经济及金融等领域的非线性随机动力学问题。
结论摘要：
英文主题词non-Gaussian stochastic excitation, nonlinear system, response, stochastic stability, reliability
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期刊论文
Stochastic stability of Duffing oscillator with fractional derivative damping under combined harmoni
The First Passage Failure of SDOF Strongly Nonlinear Stochastic System with Fractional Derivative Da
First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white nois
Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed fee
Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric un
Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined har
Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feed
Stochastic optimal bounded control of MDOF quasi nonintegrable-Hamiltonian systems with actuator sat
STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WIT
Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping unde
First-passage failure of quasi linear systems subject to multi-time-delayed feedback control and wid
First-passage failure of strongly nonlinear oscillators under combined harmonic and real noise excit
Stochastic Hopf bifurcation of quasi-integrable Hamiltonian systems with time-delayed feedback contr
Stochastic averaging of strongly nonlinear oscillators under combined harmonic and wide-band noise e
Asymptotic Lyapunov stability with probability one of quasi-integrable Hamiltonian systems with dela
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