非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究

Mean first-passage time and stochastic resonance in an asymmetric bistable system driven by non-Gaussian noise

研究了乘性非高斯噪声和加性高斯白噪声共同激励下非对称双稳系统的平均首次穿越时间和随机共振问题.利用路径积分法和两态模型理论,推导出平均首次穿越时间和信噪比的表达式.研究结果表明:势阱非对称性对两个不同方向的平均首次穿越时间的影响是不同的.信噪比是加性噪声强度和势阱非对称性的非单调函数,系统出现了随机共振现象;信噪比是乘性噪声强度的单调函数,没有共振峰出现.这说明该系统中乘性噪声强度和加性噪声强度对信噪比的影响是不同的.

In this paper,mean first-passage time （MFPT） and stochastic resonance （SR） are investigated in an asymmetric bistable system driven by multiplicative non-Gaussian noise and additive Gaussian white noise.Using the path integral approach and two-state theory,the expression of MFPT and the signal-to-noise ratio （SNR） are derived.The results show that the influences of the asymmetric coefficient on the MFPTs in two opposite directions are entirely different.SNR is a non-monotonic function of the additive noise intensity and asymmetric coefficient,therefore,an SR is found in this system.Whereas SNR is a monotonic function of the multiplicative noise intensity and no SR appears.This demonstrates that the effect of the multiplicative noise intensity on SNR is different from that of the additive noise intensity in the system.