具有功能性反应的微分生态模型的极限环分析

在已有的功能性反应生态系统的基础上,应用数学生态学理论建立了一个具有功能性反应的微分生态系统,并应用微分方程定性理论,讨论了该微分生态系统.研究了系统的平衡点,对中心焦点的阶数和稳定性做出了分析,并给出了系统的环域构成图.在给定参数满足一定条件时,利用Poincaré-Bendixson环域定理和Filippov变换,证明了该系统极限环的存在性和唯一性.结果表明,两种群的密度或产生周期性的变化,或都稳定在一组定值的附近,可以保持一种稳定状态.

Limit Cycle Analysis of a Differential Ecosystem with Functional Response

Based on ecosystem with functional response,a differential ecosystem with functional response is established with the application of mathematics ecology.The system is discussed by using differential equations qualities theory.The system’s equilibrium points are studied.The degree and the stability of the center focus are analysed.The existence zone of the system’s limit cycle is given.By using Piocare-Bendixson theorem and Filippov transformation,the existence and uniqueness of the system’s limit cycle are proved in the case that the given parameters satisfy certain conditions.It shows that the densities of preys and predators are stable under some conditions.