Fixed points and boundary layers in asymmetric simple exclusion processes

In this paper, we show how a fixed-point-based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we choose a two-species ASEP which has interesting phase transitions not seen in the one-species case. We also apply this method to the single-species problem where the analysis is simple but nevertheless quite insightful.