Traveling Wave Solutions In Delayed Predator-prey Systems With Stage Structure And Nonlocal Diffusion

There is a long history on theory of differential equation and a great results are re-searched so far. With the development of modern society, it is widely used in biological science. Traveling wave solutions play an important role in mathematical theory and prac-tical application. Therefore in recent years the research on the existence of traveling wave solutions to predator-prey system becomes the concerning subject of domestic and foreign scholars. However, the existing research has only considered predator-prey systems with non-local diffusion, and has not considered stage structure. Motivated by the above backgrounds, in this thesis we shall study traveling wave solutions in delayed predator-prey systems with nonlocal diffusion and stage structure.Chapter1introduces first the research background and current situation of the research on delayed predator-prey. In particular, we summarize the existing work on the existence of traveling wave solutions for the predator-prey systems. Then, this chapter also presents the research contents and methods in this thesis.Using upper and lower solutions methods and Schauder fixed point theorem, Chapter2shows sufficient conditions ensuring the existence of traveling wave solutions to the following delayed predator-prey systems with nonlocal diffusion and stage structureChapter3considers the following predator-prey systems, as a special case of the above system, We give the upper solutions and lower solutions of this system. Then by using the main results in Chapter2, this system exists traveling wave solutions. Therefore, the results in Chapter2are feasible.