延时对色关联噪声诱导的逻辑生长过程的影响

应用小延时近似方法，研究了色关联噪声诱导的延时逻辑生长过程，得到了肿瘤细胞数的稳态概率分布P_st(x)的近似解析表达式，发现延时τ的变化可以使P_st(x)发生由多极值结构向单极值结构的转换，延时τ还可以使随机系统的平均值〈x〉、二阶矩〈x²〉、归一化涨落V_ar的极值位置和极值大小发生改变. 关键词： 逻辑生长过程 延时 关联色噪声 统计性质

Influences of time delay on logistic growth process driven by colored correlated noises

The small time-delay approach is applied to logistic growth model when time-delayed feedback and colored correlated noises are included in the system. The steady state probability distribution P_st(x) of the tumor cell number is obtained. It is found that a configuration transition of multiple peaks to a single peak occurs due to the variation of delay time τ. An extremum appears in the curves of the mean of the steady-state tumor cell number 〈x〉, the second moment 〈x²〉, and the normalized variance V_ar versus λ. The positions and the peak values of the extrema can be effected by the time delay.