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色关联的色噪声驱动的分段非线性模型的平均首次穿越时间*
The mean first-passage time for piecewise nonlinear system driven by colored correlated additive and multiplicative colored noises*
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摘要: 研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中，噪声强度和相关时间对平均首次穿越时间的影响。利用一致有色噪声近似方法和最速下降方法，推导出系统平均首次穿越时间的表达式。研究结果表明：系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构，即“共振”现象，峰值会随着加性噪声强度和噪声之间关联强度的增加而减小。而平均首次穿越时间作为加性噪声的函数呈单调曲线，说明乘性噪声和加性噪声对平均首次穿越时间的影响不同。此外，乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时对系统平均首次穿越时间的影响是不同的。Abstract: In this paper, We have studied the effects of intensity and correlation time of noises on the mean first-passage time in a picecewise nonlinear system driven by multiplicative and additive colored noises with colored cross-correlation. We derived the expression of the mean first-passage time (MFPT) by applying the unified colored approximation method and the steepest-descent approximation. Results show that the MFPT of the system exhibits a mono-peak structure and the “resonance” phenomena enhance with the increase of multiplicative noise intensity. The value of the peak decreases with increasing additive noise intensity and the correlation between the additive and multiplicative noises. However, the MFPT of the system increases with the increase of additive noise intensity. That is, the effects of the additive noise and the multiplicative noise on MFPT are different. Moreover, the negative and passive correlations play different roles in the MFPT.
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