非高斯Lévy噪声驱动下的非对称双稳系统的相转移和平均首次穿越时间

摘要

研究了非高斯Lévy噪声激励下非对称双稳系统的相转移和首次穿越问题.首先利用Grünwald-Letnikov有限差分方法数值求解系统所对应的分数阶Fokker-Plank方程,得到了系统的稳态概率密度函数.然后分析了系统的非对称参数以及噪声强度和稳定性指标对稳态概率密度函数的影响,发现了非对称参数和稳定性指标的变化都能够诱导系统发生相转移.进一步研究了系统的平均首次穿越时间,得到了非对称参数、噪声强度和稳定性指标影响系统平均首次穿越时间的不同作用机理.%This paper aims to investigate an asymmetric bistable system driven by non-Gaussian Lévy noise.The stationary probability density functions are obtained by the Grünwald-Letnikov scheme,and the effects of noise intensity and stability index on the stationary probability density are examined.Phase transitions can be observed though a qualitative change of the stationary probability distribution,which indicates that the phase transitions are induced by the asymmetric parameter and the stability index of Lévy noise.Additionally,the mean first passage time is considered,and different mechanisms for the effects of asymmetric parameter,noise intensity and stability index on first passage time are also obtained.