The Qualitative Analysis Of Biological Systems With Allee Effect

This paper studies a predator-prey system with ratio-dependent functional response and Allee effect, a three-species of food chain model with its first trophic level contains Allee effect and ratio-dependent functional response related to the density of food and prey. Using Mawhin coincidence degree theory, this paper proves these models have at least one positive periodic solution. Using Lyapunov theory, this paper attains some sufficient conditions which guarantee the global attractivity of the positive periodic solution for the systems.