Study on Periodic Solution of Food-chain Model with Efficiency of Resources Utilization for Prey Population

The persistence,stability and the existence of positive almost periodic solutions of an ecological system is the important direction of mathematical ecology research.It has been an important topic to give a definite criterion of these upper properties of food-chain model for prey population,and many scholars have paid more attention to this field.In this paper,we investigate a food-chain model with efficiency of resource utilization for prey population.First,we obtain the sufficient conditions for permanence and prove the existence of positive periodic solution by using Brouwer theory;Furthermore,we prove the uniqueness and the globally asymptotical stability of positive periodic solution.