| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 100 === In this thesis, we review the investigations of dynamics for Lotka Volterra models and patch models in mathematical ecology. We study two open questions posed by Gourley and Kuang in 2005, which are concerned with how dispersal rates affect the competition in two-species patch model with various spatial distribution of their growth rate.
It was conjectured that, in a high dispersal environment, the winning strategy for species depends on the growth rate in a single patch. That is, the species which has the greatest growth rate will win. On the other hand, the system may have a globally asymptotically stable positive equilibrium for a small enough dispersal rate.
We have not solved the conjectures, but have better understanding on these issues.
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