Approaches to the description of spatial dynamics of migration-related populations

In this paper we consider two approaches to the description of spatiotemporal dynamics of migration-related populations, based on the coupled ordinary differential equations lattice and the system of coupled lattice maps. In the first case, spatial dynamics has a rather monotonous character, and its trajectory converges in the single nontrivial steady state. In the second case the dynamics is more complex and has periodic and irregular modes, while fluctuations in the population size can be either synchronous or asynchronous.