The Effect Of Dispersal On Some Continuous And Discrete Population Models

In this dissertation we study two mathematic ecological model with dispersal, considering the effect of the dispersal on their dynamics, respectively. The continuous competitive model in two patches is firstly considered. We obtain some conditions under which the dispersal system is permanent or extinction. Differing from the former studies, the growth rate is extended to be a general continuous function. The conditions are better than [14] by some skillful calculating.The second model is a discrete system in n-patches environment. We illustrate the single species live in n patches connected by dispersal. Utilizing the monotonic theorem we get the condition to guarantee the existence and uniqueness of the positive equilibrium. Then we consider its stability. Finally, through a two patches example, we analyze all the equilibria and give some numerical results.