具有Holling-Tanner Ⅲ类功能反应干扰系统的全局稳定性

Global Stability of a Mutual Interference System with Functional Response of Holling-Tanner Type Ⅲ

关键词:  Holling-TannerⅢ类功能反应  持久性  周期解  全局稳定性

Key words:  Holling-Tanner type Ⅲ  persistence  periodic solution  gobal stability

摘要:

对具有Holling-TannerⅢ类功能性反应的Leslie捕食与被捕食模型引入干扰常数,得到具有Holling-TannerⅢ类功能性反应和干扰的非自治Leslie捕食系统,然后,先利用微分方程定性理论证明该系统在适当条件下是持久的,再利用泛函分析的Brouwer不动点定理和构造Lyapunov泛函的方法得到该系统正周期解存在且全局渐近稳定的充分条件.

Abstract:

A class of non-autonomous mutual interference system with functional response of holling-tanner type Ⅲ is obtained with an interference constant being introduced to the Leslie pedeter and preyer model with functional response of holling-tanner type Ⅲ.It is proved by differential equation qualitative theory that the system is permanent under proper conditions.By Brouwer fixed point theory and constructing a suitable Lyapunov functional, the sufficient conditions are established for the global asymptotic stability of the periodic solution for the system.