食饵种群具有Smith增长的Holling-Ⅱ类功能性反应捕食-食饵模型  

A predator-prey model of Holling-Ⅱfunctional response for prey species with Smith growth

作　　者：俞美华[1] 

机构地区：[1]东南大学成贤学院基础部,江苏南京210088

出　　处：《高师理科学刊》2015年第5期18-22,共5页Journal of Science of Teachers＇College and University

摘　　要：建立了一类食饵种群具有Smith增长的Holling-Ⅱ类捕食-食饵模型.运用微分方程稳定性理论研究了模型平衡点的稳定性,并得到平衡点全局渐近稳定的充分条件.利用环域定理证明了稳定极限环的存在性.对结论进行了生态解释,并且运用Matlab对平衡点的稳定性进行了仿真.Constructed a predator-prey model with Smith growth of prey species and Holling-Ⅱ functional response. Studied the stability of the equilibriums, gave the sufficient conditions of globally asymptotically stable for the equilibriums by the stability theory of ordinary differential equation. Then, the existence of a stable periodic solution was proved by ring theory. The ecological significances for the above conclusions were explained and the stability of the equilibriums are illustrated by Matlab.

关 键 词：稳定性 Smith增长 捕食-食饵模型 Holling-Ⅱ类功能性反应 

分 类 号：O175.1[理学—数学] Q141[理学—基础数学]