具有资源利用率的三种群食物链系统的研究

生态系统的持久性,稳定性及概周期解的存在性问题是数学生态学理论中的一个重要研究方向。对于一些三种群食物链系统,给出上述性质的明确判定准则是数学生态学的一个重要课题,受到理论生态学家与数学家的广泛重视。研究食饵种群具有资源利用率的三种群食物链模型。首先,给出系统一致持久的充分条件,利用Brouwer不动点理论证明了系统正周期解的存在性,进一步证明了在适当条件下,系统正周期解的存在唯一性和全局渐近稳定性。

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.