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精确计算了关联时间为τ1和τ2的两相关O-U噪声所驱动线性系统的关联函数、功率谱及定态几率分布.发现:a.噪声间关联强度λ对系统的关联函数、功率谱及定态几率分布都有很大的影响;b.当驱动两O-U噪声的白噪声间的关联时间τ和两O-U噪声的自关联时间相等(τ=τ1=τ2)时,直接关联和间接关联所计算出来的关联函数、功率谱及定态几率分布是相同的;C.在完全负关联(λ=-1),且各噪声的关联时间和强度都相等时,系统的关联函数、功率谱及相对涨落变为0,即确定论情形.
The correlation function, power spectrum and the probability distribution of stationary state in linear systems driven by two correlated O-U noises with correlation time τ1 and τ2 are precisely calculated. Found: a. The correlation strength between the noise λ has a great influence on the system’s correlation function, power spectrum and the probability distribution of stationary state; b. When the correlation time τ between white noise driving two O-U noises and the self-correlation time of two O-U noises are equal (τ = τ1 = τ2), the correlation function and the power spectrum calculated by direct correlation and indirect correlation The probability distribution of steady state is the same; C. In the case of complete negative correlation (λ = -1), and the correlation time and intensity of each noise are equal, the correlation function, power spectrum and relative fluctuation of the system become 0, that is deterministic case.