Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.

平闲堂书学咀华(五)

五十六、董其昌《画禅室随笔》云:“昔人以翰墨为不朽事,然亦有遇不遇,有最下最传者,有勤一生而学之,异世不闻声响者,有为后人相倾,余子悠悠,随巨手讥评,以致声价顿减者,有经名人表章,一时慕效,大擅墨池之誉者。此亦有运命存焉。”