The influence of Gaussian colored noises on the stability of tumor-immune responses to chemotherapy system is analyzed. By means of the unified colored noise approximation of multidimensional stochastic dynamic system, the system is changed into the stochastic system with Gaussian white noises. I derive the analytic formula of the maximum Lyapunov exponent of system as a function of intensities and correlation times of Gaussian colored noises, then I find the noise-enhanced stability phenomenon, which is detected by the maximum Lyapunov exponent. Moreover, the correlation time τ₁ of ξ₁(t) influences the stability of steady state becomes unstable if τ₁ → 0.15, which also increases as the correlation time τ₂ of ξ₂(t) increases. These indicate that, once tumor grows, by controlling the stochastic effect in process of chemotherapy, such as Gaussian colored noises, it is possible to control the stability of the tumor, which is very important for treatment. Especially, one could regulate the correlation time τ₁ for this purpose.

分析了高斯彩色噪声对肿瘤对化学疗法免疫反应稳定性的影响。通过多维随机动力系统的统一有色噪声逼近，将该系统转换为具有高斯白噪声的随机系统。推导了系统最大李雅普诺夫指数作为高斯色噪声的强度和相关时间的函数的解析公式，然后发现了由最大李雅普诺夫指数检测到的噪声增强的稳定现象。此外，相关时间τ ₁的ξ ₁（吨）影响稳定状态的稳定性变得不稳定，如果τ ₁ →0.15，这也增加作为相关时间τ ₂的ξ ₂（吨）增加。这些表明，一旦肿瘤生长，通过控制化学疗法过程中的随机效应，例如高斯色噪声，就有可能控制肿瘤的稳定性，这对于治疗非常重要。特别是，人们可以调节相关时间τ ₁用于此目的。