Bistable Waves For A Single Species Model In 2-Dimension Lattice

Population ecology is one of the most widely applied and also the most systematically and maturely developed branches of mathematics in ecology,which mainly studies the relationship between biological population and environment.As a basic model of population ecology,the single population model reveals the variation rule of a population density with time.Many studies of population models can be come down to the study of reaction-diffusion equation.However,due to the differences in climate and topographical factors in different regions in nature,the distribution patterns of populations in different environments are also varied.This prompted us to study the dynamics of more populations in different environments and regions.This thesis studies the bistable traveling waves for a single species model with age structure and a fixed maturation period in a two-dimension lattice strip.First,the existence and uniqueness of the solution of the initial value problem of the model are proved by using the fixed point theorem of compression and the comparison principle is established.Then,by means of the corresponding linear problem,we obtain the existence of bistable traveling waves of the model,and by constructing various pairs of super-and subsolutions,employing the squeezing technique to prove the uniqueness with phase shift and globally exponential stability of bistable traveling waves.