Effects of Perfectly Correlated and Anti-Correlated Noise in a Logistic Growth Model

The logistic growth model with correlated additive and multiplicative Gaussian white noise is used to analyze tumor cell population. The effects of perfectly correlated and anti-correlated noise on the stationary properties of tumor cell population are studied. As in both cases the diffusion coefficient has zero point in real number field, some special features of the system are arisen. It is found that in both cases, the increase of the multiplicative noise intensity cause tumor cell extinction. In the perfectly anti-correlated case, the stationary probability distribution as a function of tumor cell population exhibit two extrema. (general)