Spatial Patterns for Population Models in a Heterogeneous Environment

In this paper, we review some recent results on the effects of heterogeneous spatial environment on various population models. By making use of the observation that the population models make deep changes of behavior when certain coefficient functions vanish in the underlying domain, it is shown that sharp stable patterns can be obtained if the heterogeneous environment is designed suitably. The one species logistic model, two species competition and predator-prey models are discussed.