(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this survey we discuss some recent progress on the ideal free distribution theory in patch models, with the emphasis on two patches. We show that dispersal strategies leading to the ideal free distributions of organisms are generally evolutionarily stable. We will also study the existence of evolutionarily stable dispersal strategies when dispersal strategies do not lead to the ideal free distributions. Applications to some river models are given.