The Existence Of Solutions For Predation And Competition Models With Tendency

Bio-mathematics is a branch of mathematics. It's a very important subject to research biologic problems in mathematical way,with the help of modeling. All species in the nature have made up a complicated but regular food chain,in which style,one kind of specie maybe the food of another ones just because of living. This phenomenon is called predation as we all know.The study of this kind of problems is very applied, in the help of which,we can learn much more about the change of some species as the amount of their food is changing. For example,relying on the fact that the injurious insects are fond of the crops,,people can kill lots of injurious insects in the way of spraying agricultural chemical on crops,in order to get bumper harvest in the next year.Compared with the traditional predation model, the factors that this thesis consid-ers are not only the diffusion,division and death of species,but also the stress reaction of species in feeding and catching behavior, which is very important and hasn't been discussed in the traditional predation model.Moreover, we also consider another element in this paper,which is called competition.In our new model,we add another equation in order to discuss the problem that two different species both catch some one kind of specie.This thesis mainly discuss the existence of the solution of this predation and competition model.