title: Modelling population growth with delayed nonlocal reaction in 2-dimensions.
abstract: In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-difusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining diferent boundary conditions. The important feature of the models is the reflection of the joint efect of the difusion dynamics and the nonlocal maturation delayed efect. We consider and ana- lyze numerical solutions of the mature population dynamics with some wellknown birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the efects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.
authors.affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3. dliang@math.yorku.ca.
authors.forename: Dong
authors.initials: D
authors.lastname: Liang
authors.forename: Jianhong
authors.initials: J
authors.lastname: Wu
authors.forename: Fan
authors.initials: F
authors.lastname: Zhang