色噪声和周期激励下肿瘤细胞增长系统的随机共振

Stochastic Resonance in a Tumor Cell Growth System Driven by a Colored Noise and Periodic Excitation

本文研究了色噪声驱动下肿瘤细胞增长系统的随机共振现象,根据Novikov定理和统一色噪声理论,得到了相应的FPK方程,并给出了稳态概率密度函数的表达式。运用绝热近似理论,得到了信噪比的解析表达式。结果表明,在噪声强度较小时产生了随机共振,且其强度随着增长率和周期作用振幅的增大而增强,而承载能力对随机共振强度没有显著影响,但承载能力越大,要达到共振所需要的噪声强度也越大。

In this paper, stochastic resonance in a tumor cell growth system driven by a colored noise and periodic excitation is investigated. According to Novikov theorem and unified colored noise theory, the related Fokker-Plank equation and the stable probability density function are obtained. Based on theory, we present the explicit expression of signal-to-noise ratio. Conclusions are that: stochastic resonance produced as noise strength is little and its strength is increased as tumor cell growth rate and amplitude of periodic effect are increased respectively. But the carrying capacity has no obvious impact on the strength of stochastic resonance, however, the more carrying capacity is, the more the required noise strength to attain stochastic resonance is.