交叉关联噪声与时间延迟对肿瘤细胞生长过程的影响

Effects of Time-Delay and Cross-Correlated Noises on the Tumor Cell Growth Process

运用随机数值模拟方法,研究了内噪声和外噪声驱动的时滞Logistic模型描述的肿瘤细胞生长系统的瞬态性质.数值模拟结果表明,噪声间的关联强度λ、系统的延迟时间τ、乘性噪声强度α的增大均能使系统的平均首通时间T下降,即加速肿瘤细胞的消亡过程,降低系统的稳定性;在时间延迟与关联噪声的相互作用下,随着τ的增大,出现了τ抑制λ和α对肿瘤细胞衰减过程加速作用的现象;此外,噪声间的负关联也能抑制较大的τ和较小的τ对T的影响.

Based on the time-delayed Logistic model,taking the influences of the fluctuating environmental factors on the tumor cell growth into account,an additive noise and a multiplicative noise are introduced into the model and a stochastic delayed differential equation is obtained to describe the tumor cell growth process.The effects of the delay time(τ) and the cross-correlation strength(λ) between the multiplicative noise(α) and the additive noise(D) on the mean first passage time(T) of the system are studied by the numerical simulation method.It is found that the parameters τ,λ,and α can speed up the process of the tumor cell extinction.In addition,with τ increasing,it can restrain the effects of λ and α on T.The λ can also suppress the effect of the small τ and the large τ on T for the case of the negative cross-correlation.