Asymptotic profile of a mutualistic model on a periodically evolving domain

In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.