关联白噪声驱动的具有时间延迟的Logistic系统

关联白噪声驱动的具有时间延迟的Logistic系统可更真实的反映肿瘤细胞的增长问题，本文通过小时间延迟近似方法对由关联白噪声驱动的具有时间延迟的Logistic系统进行了研究，得到了系统的稳态概率密度，并进一步分析了加性和乘性噪声强度，噪声关联时间和时间延迟对稳态概率密度的影响以及噪声诱导的非平衡相变现象. 关键词： Logistic系统 关联白噪声 时间延迟 非平衡相变

Time-delayed Logistic system driven by correlated Gaussian white noises

Time-delayed Logistic system driven by correlated Gaussian white noises could be a more true reflection of the growth of tumor cell population. In this paper, we study the Logistic system through the small time delay approximation to obtain the probability density of the system in its steady state, and further analyze the influences of the additive and multiplicative noise intensity, the noise-correlated time and the time delay on the steady-state probability density. The non-equilibrium phase transition phenomena induced by the noises is also studied.