Some Properties Of The Three Group Mutual Model Parabolic Systems Solutions

Mathematical Ecology is the study of ecology that uses mathematical models to help predict and interpret what we observe. It is a fast growing, well recognized subject and is the most exciting modern application of mathematics.This dissertation is devoted to various nonlinear partial differential systems established in ecology. In the last few years , a lot of effort has been devoted to the study of the two-species Lotka-Volterra models. The properties of solutions to the corresponding partial differential equations are well-knows. We will study the three species Lotka-Volterra models.Frist, we consider a parabolic system describing three populations in cooperating modelthe global existence and blowup results of solution are given by upper and lower solutions. It is shown that global solution exists if the intra-specific competitions are strong, whereas blowup solution may exist if the intra-specific competitions are weak. We also consider a parabolic system in a three species mutualistic modelIt is shown that any solution with time delays is global. It is also shown by the method of upper and lower solutions that the solution without time delays is global if the competition is stronger than the cooperation among three species, otherwise the solution may blow up.