The effect of diffusion on the time varying logistic population growth

In this paper, we consider the effect of diffusion on the species that live in changing patches environment. Different from the former studies [1–4], we pay attention to the more important situation in conservation biology that species live in a weak patches environment, in the sense that species in some of the isolated patches will be extinct without the contribution from other patches. We obtain an interesting result: the identical species can persist for some diffusion rates, and can also vanish for another set of restriction on diffusion rates.