色交叉关联噪声作用下癌细胞增长系统的平均首通时间

研究了受色交叉关联噪声驱动的癌细胞增长系统的平均首通时间.根据Novikov定理和Fox方法得到了相应的近似Fokker-Planck方程,给出了稳态概率密度函数的表达式.运用最快下降法,得到了平均首通时间的解析式.数值结果表明:两噪声之间负关联时,平均首通时间是加性噪声强度和乘性噪声强度的减函数,是噪声关联时间的增函数;两噪声之间正关联时,平均首通时间与加性噪声强度之间的单调关系与穿越方向有关,是乘性噪声强度的非单调函数,是噪声关联时间的减函数.

The mean first-passage time for a cancer development system driven by colored cross-correlated noises

In this paper, the mean first-passage times for a cancer development system driven by colored cross-correlated noises are investigated. Based on the Novikov theorem and the Fox approach, the approximate Fokker-Planck equation and the explicit expressions of the mean first-passage time are derived. Numerical results show that: if the coupling strength between the two noises is negative, the mean first-passage time is a decreasing function of the two noise intensities, but an increasing function of the correlation time; if the coupling strength between the two noises is positive, then the value of the monotonic mean first-passage time versus the additive noise intensity depends on the transition direction. And in addition, the mean first-passage time is a non-monotonic function of the multiplicative noise intensity, but a decreasing function of the correlation time.