Study On Some Lotka-Volterra Predator-prey Models

In recent years, population ecology has become one of the most popular themes. By making some mathematical models and using some mathematical knowledge, researchers obtain many biological characters of species. This method takes an important part in de-velopment of ecology. The models studied most are Lotka-Volterra systems. With the development of mathematical ecology, Lotka-Volterra is also further spread and improved. In these models, more practical factors are considered so that these models are more accurate to represent the practical interact of species.This paper studies some Lotka-Volterra predator-prey systems with continuous delay. This paper is divided into four chapters:Chapter one outlines the historical development of population ecology and the related work done by their predecessors.Chapter two discusses a n+m-species Lotka-Volterra predator-prey systems with con-tinuous delay: by using of cone fixed point theory, we obtain the sufficient condition for the existence of one positive periodic solution.Chapter three discusses a class of 2-species Lotka-Volterra predator-prey systems with mutual interference and continuous delay: using the coincidence degree theory, we obtain the sufficient condition for the existence of one positive periodic solution.Chapter four discusses a class of 3-species Lotka-Volterra predator-prey systems with mutual interference: by making Liapunov function, we obtain the sufficient condition for globally asymptotically stable of the systems.